Question

What is the first term of the geometric sequence presented in the table below?

n 3 8
an 112 −3,584


Hint: an = a1(r)n − 1, where a1 is the first term and r is the common ratio.
a1 = −28
a1 = −2
a1 = -1/2
a1 = 28

Answer 1

Fron the table given:

A3 = 112,
A8 = - 3,584

An = A1 *r ^ (n-1)

=> A3 = A1 (r^2) = 112

A8 = A1(r^7) = - 3,584

=> - 3584 / 112 = (r^7) / (r^2)

=> (r^5) = - 32

=> r = - 2

=> A1 (- 2)^2 = 112

=> A1 = 112 / 4 = 28

Answer: a1 = 28