Question

Given two terms in a geometric sequence find the term named:
a 5= -324 and a2=12 Find a 9

Answer 1

To find the ninth term of a geometric sequence with given terms, we found the common ratio and then calculated the ninth term using the formula for the nth term in a geometric sequence, yielding a9 = -26244.

Step-by-step explanation:

To determine a9 in the geometric sequence, we need to find the common ratio (r) between consecutive terms. We know that a5 = -324 and a2 = 12. Recall the formula for the nth term of a geometric sequence: an = a1 × r(n-1). To find 'r', we use the relationship a5 = a1 × r4.

First, let's express a5 in terms of a2:

a5 = a2 × r3

Solving for 'r' gives us:

r3 = a5 / a2 = -324 / 12 = -27

So the common ratio 'r' is the cube root of -27, which is r = -3.

Now, we can find a9 using the common ratio:

a9 = a1 × r8 = a2 / r × r8 = 12 / -3 × (-3)8

Calculating a9:

a9 = -4 × 6561 = -26244

Therefore, the ninth term of the geometric sequence is -26244.