The first Last term of an arithmetic progression are 7 and 43 respectively. The sum of the terms of the progression is 250 Find the number of terms and common difference of the progression

The formula for the sum of an arithmetic progression when the first and last terms are known is:
Sₙ = (n/2)(a + L)

Substitute the given values into the formula:
250 = (n/2)(7 + 43)
250 = (n/2)(50)
Multiply both sides by 2:
500 = n × 50
Divide by 50 to find n:
n = 500 / 50
n = 10

The formula for the last term of an arithmetic progression is:
L = a + (n - 1)d

Substitute the known values (a, L, and the n we just found) into the formula:
43 = 7 + (10 - 1)d
43 = 7 + (9)d
Subtract 7 from both sides:
43 - 7 = 9d
36 = 9d
Divide by 9 to find d:
d = 36 / 9
d = 4

The number of terms is 10 and the common difference is 4.