Question

What is a formula for the nth term of the given sequence?
-17, -8, 1...
−17,−8,1...

a_{n}=-8+9(n-1)a
n
​
=−8+9(n−1)
a_{n}=-17(9)^{n}a
n
​
=−17(9)
n

a_{n}=9n-26a
n
​
=9n−26
a_{n}=-17-9(n-1)a
n
​
=−17−9(n−1)

Answer 1

Answer:

The nth term of the given arithmetic sequence is $a_n=-17+(n-1)9$

Step-by-step explanation:

Given sequence is -17,-8,1,...

To find the nth term of the given sequence :

Let  $a_1=-17,a_2=-8,a_3=1,...$

To find the common difference d :

$d=a_2-a_1$

$=-8-(-17)$

$=-8+17$

Therefore d=9

$d=a_3-a_2$

$=1-(-8)$

$=1+8$

Therefore d=9

The common difference d is 9

Therefore the given sequence is an arithmetic sequence

The nth term of an arithmetic sequence is given below

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

Substitute $a_1=-17$ and d=9 in the above equation we get

$a_n=-17+(n-1)9$

Therefore the nth term of the given arithmetic sequence is $a_n=-17+(n-1)9$