Sequence Math Question

Question

The first term of a sequence is -48, and every term after the first is 3/4 of the previous term. What is the 7th term of the sequence?

Answer 1

Since every term after the first is 3/4 of the preceding term, the sequence is geometric with common ratio

r = 3/4.

The nth term, a_n, is given by a_n = a₁r^n-1.

So, the seventh term = a₇ = -48(3/4)⁶ = -34992 / 4096 = -2187/256