The common difference in the arithmetic progression is approximately 8.70.
How to solve
Given:
First term (a) = 7
Last term (l) = 77
Sum of the AP (S) = 380
Formula for the sum of an AP:
S = n/2 * (a + l)
We would substitute the values here:
380 = n/2 * (7 + 77)
380 = n/2 * 84
760 = n
n = 9.0476
The formula for the common difference (d):
d = (l - a) / (n - 1)
We would substitute the valuesa
d = (77 - 7) / (9.0476 - 1)
d = 70 / 8.0476
d ≈ 8.70 (rounded to two decimal places)
Therefore, the common difference in the arithmetic progression is approximately 8.70.