Question

HELP ASAP 40 POINTS

Answer 1

Given:

The sequence is -8, -12, -16.

To find:

The nth and 52th term  of the given sequence.

Solution:

We have,

-8, -12, -16

It is an AP because the difference between consecutive terms are equal. Here, first term is -8 and the common difference is

$r=a_2-a_1$

$r=-12-(-8)$

$r=-12+8$

$r=-4$

The nth term of an AP is

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

Where, a is first term and d is common difference.

Putting a=-8 and d=-4, we get

$a_n=-8+(n-1)(-4)$

$a_n=-8-4n+4$

$a_n=-4-4n$

Putting n=52, we get

$a_{52}=-4-4(52)$

$a_{52}=-4-208$

$a_{52}=-212$

Therefore, the equation for the nth term of the given sequence is $a_n=-4-4n$ and the 52nd term of the sequence is -212.