Write a formula for the general term or nth term for the giv

Write a formula for the general term, or nth term, for the given, -4, 20, -100,5000,... a_n = -4(-5)^n -1 a_n = -4 + (-5)^n a_n = -4(-5)^n a_n = -20^n - 1 1, 2/3, 1/3, 2/15,... a_n = 2n + 1/n! a_n = 2^n/n! a_n = 2n/(n + 1)! a_n = 2^n/(n + 1)!

Solution

(1) -4, 20, -100,500

Common Ratio = 20/-4=-100/20...= -5

Geomtric progression nth term = ar^n-1

a= first term,

r= common ratio.

So nth term of given equation = -4 (-5)^n-1 ...Option A is the correct answer

(2) 1, 2/3,1/3, 2/15...

we can write the same series as 2/2, 4/6, 8/24, 16/120

All numerators are in the form of 2^n and denominators in the form of 2!,3!,4!,5!

so nth term can be written as =2^n/(n+1)!.. Option D is the correct answer