Question

Find the specified value for the arithmetic sequences with the given characteristics. a17 = 47 d = -3 a35= ?

Answer 1

ANSWER

The 35th term is -8

EXPLANATION

The nth term of an arithmetic sequence is given by

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

We have the 17th term to be;

$a_{17}=47$

and the common difference is d=-3

We substitute to get:

$47= a_1 + - 3(1 7- 1)$

$47= a_1 + 16( - 3)$

$47= a_1 - 48$

$a_1 = 48 + 47 = 95$

We can now find the 35th term:

$a_{35}=a_{1} + 34d$

$a_{35}=95 + 34( - 3) = - 8$