Use the simplest rule you can find to calculate the next three terms of the following sequence.

15, 24, 35, 48, 63, ...

A. 126, 252, 504

B. 80, 99, 120

C. 48, 35, 15

D. 82, 90, 98

B

Step-by-step explanation:

If you look closely 24 minus 15 is 9 and 35 minus 24 is 11. The sequence is basically adding 2 to every difference between each number. so just add 17 to 63 because the 2 numbers before had a difference of 15 and so on so forth.

15, 24, 35, 48, 63, ...

a1 = 15

a2 = a1 + 2 * 4 + 1 = 15 + 9 = 24

a3 = a2 + 2 * 5 + 1 = 24 + 11 = 35

a4 = a3 + 2 * 6 + 1 = 35 + 13 = 48

a5 = a4 + 2 * 7 + 1 = 48 + 15 = 63

and so on

so

an = a (n - 1) + 2 (n + 1) + 1

a6 = a5 + 2 (6 + 2) + 1 = 63 + 16 + 1 = 80

a7 = a6 + 2 (7 + 2) + 1 = 80 + 18 + 1 = 99

a8 = a7 + 2 (8 + 2) + 1 = 99 + 20 + 1 = 120

Next 3 terms should be 80, 99, 120

Answer

B. 80, 99, 120