Question

Write an explicit formula for each sequence and find the 7th term for each

1. -4, 12, -36
2. 12, 3, 3/4

Answer 1

1. a[n] = -4·(-3)^(n-1); -2916
2. a[n] = 12·(1/4)^(n -1); 3/1024

Explanation:

You want the explicit formula for each of the geometric sequences, and the 7th term.

1. -4, 12, -36
2. 12, 3, 3/4

Explicit formula

The explicit formula for a geometric sequence with first term a[1] and common ratio r is ...

a[n] = a[1]·r^(n-1)

1. a[1] = -4, r = -3

The explicit formula is ...

a[n] = -4·(-3)^(n-1)

The 7th term is ...

a[7] = -4·(-3)^(7-1) = -2916

2. a[1] = 12, r = 1/4

The explicit formula is ...

a[n] = 12·(1/4)^(n -1)

The 7th term is ...

a[7] = 12·(1/4)^(7-1) = 3/1024