Question

Find the 21st term of the sequence 15,8,1,-6

Answer 1

-125

Explanation:

Each term is 7 less than the previous term.

1st term: 15

2nd term: 15 - 7

3rd term: 15 - 7 - 7 = 15 - 2(7)

4th term = 15 - 7 - 7 - 7 = 15 - 3(7)

Notice that each term is 15 minus a multiple of 7. The multiple is obtained by multiplying 7 by 1 less than the term number.

The formula is:

`a_n = 15 - 7(n - 1)`

For the 21st term, multiply 7 by 20, and subtract from 15.

7 × 20 = 140

15 - 140 = -125

Using the formula:

`a_(21) = 15 - 7(21 - 1) = 15 - 7(20) = 15 - 140 = -125`

Answer: -125