Question

What is the 32nd term of the arithmetic sequence where a1 = −34 and a9 = −122? (1 point)

Answer 1

Answer:

The 32nd term of the arithmetic sequence is -386.

Step-by-step explanation:

Given:   The arithmetic sequence where $a_1=-34$ and  $a_9=-122$

We have to find the 32nd term of the arithmetic sequence.

Consider the given sequence with $a_1=-34$ and $a_9=-122$

We know , For a given sequence in an Arithmetic sequence with first term $a_1$ and common difference d , we have,

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

We first find the common difference "d".

$a_9=-122$

$a_9=a_1+(9-1)d$

$a_1=-34$ , we have,

$-122=-34+8d$

Solve for d , we have,

-88= 8d

d = - 11

Thus, 32nd term is $a_{32}=a_1+(32-1)d$

$a_{32}=-34+32\cdot (-11)$

$a_{32}=-386$

Thus, The 32nd term of the arithmetic sequence is -386.