Find the indicated terms of the arthmetic sequence. Please explain how.

Question

T3=81, T12=87; determine T23.

Answer 1

Given 3rd term and 12th term in arithmetic sequence.

We know the formula for n th term = a + (n - 1)d.

Here a  = first term, d  = common difference.

Similarly T 3 = a + 2d  , T 12  = a + 11d and T 23 = a + 22d .

a + 2d  = 81 ---> (1)

a + 11d  = 87 ----> (2)

To eliminate the a value subtract equation (1) from equation (2).

a + 11d  = 87

a + 2d  = 81

(-) (-)    (-)

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9d  = 6

d  = 6/9

d  = 2/3

Substitute the d  value in equation (1).

a + 2(2/3) = 81

a + 4/3 = 81

Subtract 4/3 from each side.

a  = 81-4/3

a  = 239/3

Substitute the a , d  value in T 23.

T 23 = 239/3 + 22(2/3) = 239/3 + 44/3

T 23 = 283/3.