The sum of the first n terms of an arithmetic progression is 252. if the first term is - 16 and the last term is 72, find the number of terms and the common difference of the A. P

There are 9 terms, and the common difference is 11.

Step-by-step explanation:

The sum of the first n terms of an arithmetic sequence is:

S = n (a₁ + aₙ) / 2

where a₁ is the first term and aₙ is the last term.

252 = n (-16 + 72) / 2

n = 9

The nth term of an arithmetic sequence is:

aₙ = a₁ + d (n-1)

where d is the common difference.

72 = - 16 + d (9-1)

d = 11

There are 9 terms, and the common difference is 11.