Find the sum of the first 10 terms of the following arithmetic progressions.

Question

Find the second term of a geometric progression for which a₄=4 and a₄=-108

Answer 1

I'm going to assume you mean that a1 = 4 and a4 = -108.

 

The formula for a geometric sequence is:

a_n = a₁*r^n-1

 

Since they gave us a₁ = 4, we can use a₄ to find the common ratio, r.

 

a₄ = 4*r^4-1

-108 = 4*r³

-27 = r³

Cube root -27 to get that r = -3.

 

To find a₂, you can multiply a₁ by -3 to get a₂ = 4*(-3) = -12.