3 questions

Question

 

Find the 10^th term of the sequence whose n^th term is given by the formula t_n = (-1)ⁿ⁺¹/n.

	A.	-1/10
	B.	-1/7
	C.	1/7
	D.	1/10

Find S₁₅ for 1 + 1.5 + 2.25 + 3.375 +...

	A.	582
	B.	732
	C.	645.21
	D.	873.79

 

Steven wants to open a savings account with $750. He is looking at 2 different accounts. The first account will earn 7% interest monthly. The second account will earn 9% interest monthly. Use the graphs to compare the amounts for each savings account.

	A.	Steven will earn more in the account with 7% interest, and as time increases, the amounts in each account will become approximately equal to each other.
	B.	Steven will earn more in the account with 7% interest, and as time increases, the amount will become increasingly more.
	C.	Steven will earn more in the account with 9% interest, and as time increases, the amount in each account will become approximately equal to each other.
	D.	Steven will earn more in the account with 9% interest, and as time increases, the amount will become increasingly more.

 

Answer 1

From the graph option D is correct.

Answer 2

1)

Find the 10th term of the sequence by using the given relation:

t_n = (-1)ⁿ⁺¹/n

Here n =10

t₁₀ = (-1)¹⁰⁺¹/10

     = (-1)¹¹/10

     = -1/10

So option A is correct.

Answer 3

The geometric series is 1 + 1.5 + 2.25 + 3.375 +...
 

where a = first term and r = common ratio.

a =1

Find the common ratio:

r = t₂/t₁

   _{= 1.5/1}

  _=1.5

_{Sum of the 15 term  by using the formula.}

S_n  = a(1- rⁿ )/(1-r)

Here, a = 1, n =15 and r =1.5

S₁₅  = 1(1- 1.5¹⁵ )/(1-1.5)

         ^{= 873.79}

So option D is correct