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Use the formula for sum of first n terms of a geometric sequence to evaluate following sum. (Hint: Find the first term a and common ratio r for each of the given sum.)

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a) 10:i=1 Σ (5^i)/(3^(i-1))

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b) 15:i=1 Σ (2^(2i))/(3^(i+1))

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(a) Find sum of first 7 terms of the geometric sequence whose 5th term is 32 and 6th term is 64.

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(b) Find sum of first 5 terms of the geometric sequence whose 4th term is 9/4 and 5th term is 27/8 .

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(c) Find sum of first 6 terms of the geometric sequence whose 2 nd term is 3 and 5 th term is 81.

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Step 1:

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The sequence is $\"\"$ .

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The termms of the sequence are:

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Substitute $\"\"$ .

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$\"\"$ .

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Substitute $\"\"$ .

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$\"\"$ .

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Substitute $\"\"$ .

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$\"\"$ .

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Therefore, the geometric sequence is sequence is $\"\"$ .

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The common ratio is $\"\"$ .

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$\"\"$ .

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The first term of the sequence is $\"\"$ .

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Sum of first $\"\"$ terms in a geometric series is $\"\"$ .

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Substitute $\"\"$ , $\"\"$ and $\"\"$ in $\"\"$ .

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$\"\"$

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$\"\"$

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$\"\"$

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$\"\"$

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$\"\"$

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The sum of the series is $\"\"$ .

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(b)

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Step 1:

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The sequence is $\"\"$ .

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The termms of the sequence are:

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Substitute $\"\"$ .

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$\"\"$ .

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Substitute $\"\"$ .

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$\"\"$ .

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Substitute $\"\"$ .

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$\"\"$ .

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Therefore, the geometric sequence is sequence is $\"\"$ .

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Find the sum of first $\"\"$ terms of the sequence.

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The common ratio is $\"\"$ .

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$\"\"$ .

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The first term of the sequence is $\"\"$ .

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Sum of first $\"\"$ terms in a geometric series is $\"\"$ .

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Substitute $\"\"$ , $\"\"$ and $\"\"$ in $\"\"$ .

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$\"\"$

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$\"\"$

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$\"\"$

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$\"\"$

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$\"\"$

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$\"\"$

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The sum of the series is $\"\"$ .

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Find sum of first 7 terms of the geometric sequence whose 5th term is 32 and 6th term is 64

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The $\"\"$ term of the geometric sequence is $\"\"$ .

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The $\"\"$ term of the geometric sequence is $\"\"$ .

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The common ratio is $\"\"$ .

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Formula for $\"\"$ term in geometric sequence is $\"\"$ .

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Find the first term of the geometric sequence $\"\"$ .

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Substitute $\"\"$ and $\"\"$ in $\"\"$ .

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$\"\"$ .

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Substitute $\"\"$ .

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$\"\"$

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$\"\"$

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$\"\"$ .

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The first term of the sequence is $\"\"$ .

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Find the sum of first $\"\"$ terms.

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The sum of first $\"\"$ terms in a geometric series is $\"\"$ .

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Substitute $\"\"$ , $\"\"$ and $\"\"$ in $\"\"$ .

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$\"\"$

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$\"\"$

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$\"\"$

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$\"\"$

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$\"\"$ .

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The sum of first $\"\"$ terms is $\"\"$ .

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) Find sum of first 5 terms of the geometric sequence whose 4th term is 9/4 and 5th term is 27/8 .

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The $\"\"$ term of the geometric sequence is $\"\"$ .

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The $\"\"$ term of the geometric sequence is $\"\"$ .

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The common ratio is $\"\"$ .

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Formula for $\"\"$ term in geometric sequence is $\"\"$ .

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Find the first term of the geometric sequence $\"\"$ .

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Substitute $\"\"$ and $\"\"$ in $\"\"$ .

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$\"\"$ .

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Substitute $\"\"$ .

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$\"\"$

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$\"\"$

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$\"\"$

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$\"\"$ .

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The first term of the sequence is $\"\"$ .

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Find the sum of first $\"\"$ terms.

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The sum of first $\"\"$ terms in a geometric series is $\"\"$ .

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Substitute $\"\"$ , $\"\"$ and $\"\"$ in $\"\"$ .

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$\"\"$

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$\"\"$

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$\"\"$

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$\"\"$ .

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The sum of first $\"\"$ terms is $\"\"$ .

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Find sum of first 6 terms of the geometric sequence whose 2 nd term is 3 and 5 th term is 81.

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The $\"\"$ term of the geometric sequence is $\"\"$ .

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The $\"\"$ term of the geometric sequence is $\"\"$ .

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Formula for $\"\"$ term in geometric sequence is $\"\"$ .

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Find the first term of the geometric sequence $\"\"$ .

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Substitute $\"\"$ in $\"\"$ .

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$\"\"$

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Substitute $\"\"$ .

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$\"\"$

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$\"\"$ .

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Substitute $\"\"$ in $\"\"$ .

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$\"\"$

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Substitute $\"\"$ .

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$\"\"$

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$\"\"$

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Substitute $\"\"$ .

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$\"\"$

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$\"\"$

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$\"\"$

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$\"\"$

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$\"\"$ .

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Substitute $\"\"$ in $\"\"$ .

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$\"\"$ .

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The first term of the sequence is $\"\"$ .

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Find the sum of first $\"\"$ terms.

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The sum of first $\"\"$ terms in a geometric series is $\"\"$ .

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Substitute $\"\"$ , $\"\"$ and $\"\"$ in $\"\"$ .

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$\"\"$

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$\"\"$

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$\"\"$

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$\"\"$ .

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The sum of first $\"\"$ terms is $\"\"$ .