Question

!!!CALCULUS!!! 20 POINTS

Write an explicit formula for the sequence {a_n}={-3, -1/2, 2, 9/2, 7, ...}. Then find a_17.
a_n=5/2*n-11/2;37
a_n=3/2*n-9/2;21
a_n=5/2*n-11/2;69/2
a_n=-5/2*n+11/2;-37

Answer 1

A is the right answer

Explanation:

Answer 2

Option A is correct.

`a_n = (5)/(2)n - (11)/(2)`

`a_(17)=37`

Explanation:

An arithmetic sequence is a sequence of number that the common difference between between the consecutive term is constant.

Explicit formula for arithmetic sequence is given by;

`a_n = a_1 + (n-1)d`

where

n is the number of terms.

`a_1` is the first term

d is the common difference.

Given the sequence :
`a_n = \{-3, -(1)/(2), 2, (9)/(2) , 7, ....\}`

This is an arithmetic sequence with common difference: d =
`(5)/(2)`

Here,
`a_1 = -3`

Since;

`-(1)/(2) - (-3) = -(1)/(2)+3 = (5)/(2)`

`2- (-(1)/(2)) = 2+(1)/(2) = (5)/(2)` and so on...

Then;

`a_n = a_1+(n-1)(5)/(2)`

or

`a_n = -3+(5)/(2)n -(5)/(2)`

Simplify:

`a_n = (5)/(2)n - (11)/(2)` .....[1]

To find
`a_(17)`;

put n =17 in [1] we get;

`a_(17) = (5)/(2)(17) - (11)/(2) = (85)/(2) - (11)/(2) = (85-11)/(2)=(74)/(2) = 37`

Therefore, the explicit formula for the given sequence is,
`a_n = (5)/(2)n - (11)/(2)` and value of
`a_(17) = 37`;