Question

7,21,63
what’s the common ratio, recursive function, explicit formula, and the 12 term

Answer 1

See explanations below

Explanation:

The given sequence 7,21,63... is geomertic in nature

The nth term is expressed as;

Tn = ar^n-1

a is the first term = 7

r is the common ratio = 21/7 = 63/21 = 3

n is the number of terms

Substitute

Tn = 7(3)^n-1

For the 12th term, when n = 12

T12 = 7(3)^12-1

T12 = 7(3)^11

T12 = 7(177,147)

T12 = 1,240,029

Hence the 12th terms is 1,240,029

For the recursive function

First term = 7(1)

2nd term T2 = 21 = 7(3)

3rd term T3 = 63 = 7(9) = 7(3^2)

Tn = 7(3^n)

Hence the recursive function is 7(3^n)