Question

these are the first six terms of a sequence with a1=5: 5, 20, 80, 320, 1280, 5120, ... find a recursive formula for this sequence that is valid for n>1. write your answer in simplest form.

Answer 1

The given sequence starts with a1 = 5 and each term is obtained by multiplying the previous term by 4. The recursive formula for this sequence is an = 4 * an-1.

Step-by-step explanation:

The given sequence starts with a1 = 5 and follows the pattern where each term is obtained by multiplying the previous term by 4. So:

1. The second term (a2) is obtained by multiplying the first term (a1) by 4, which gives 5 x 4 = 20.
2. The third term (a3) is obtained by multiplying the second term (a2) by 4, which gives 20 x 4 = 80.
3. Similarly, the fourth term (a4) is obtained by multiplying the third term (a3) by 4, which gives 80 x 4 = 320.

In general, the recursive formula for this sequence can be expressed as an = 4 * an-1, where 'an' represents the nth term of the sequence and 'an-1' represents the previous term.