Question

let a1,a2,a3...an be a geometric sequence with common ratio r. Find S8

a1= 3
a8= -384
r=-2

Answer 1

In a geometric sequence, the nth term can be found using the formula:

an = a1 * r^(n-1)

We are given that a1 = 3, so we can substitute this into the formula:

a8 = 3 * r^(8-1)

Since a8 = -384, we can set up the equation:

-384 = 3 * r^7

Now, let's solve for r:

r^7 = -384/3

r^7 = -128

Taking the seventh root of both sides:

r = -2

Now that we have the common ratio (r), we can find the sum of the first 8 terms (S8) using the formula for the sum of a finite geometric series:

S8 = a1 * (1 - r^8) / (1 - r)

Substituting the given values:

S8 = 3 * (1 - (-2)^8) / (1 - (-2))

S8 = 3 * (1 - 256) / (1 + 2)

S8 = 3 * (-255) / 3

S8 = -255

Therefore, the sum of the first 8 terms is -255.