Question

Evaluate the related series each sequence
1.2,12,72,423
2.-1, 5,-25, 125
3.-2, 6,-18, 54,-162
4.-2, -12, -72, -432, -2592
Answer key with sulotion

Answer 1

looks like each sequence is a geometric one
to find the r value, simply divide the 2nd by the first, check by doing another division
for another pair.

The formula for the sum of terms of a GP is
sum(n) = a(r^n - 1)/(r - 1)

I will do the 3rd, you repeat the same steps for the others

-2, 6, -18, 54, -162
here a = -2
r = 6/-2 = -3, check: -162/54 = -3
counting, I see 5 terms, so n = 5
sum(5) = -2((-3)^5 - 1)/(-3-1)
= -2(-243-1)/-4
= -2(-244)/-4 = - 122

btw, you can check your answers by simply adding up the terms, there are just a few of them