The sum of the first four terms of an AP is 30 and the sum of the last four terms is 66. If the AP has 7 terms, find the first term and the common difference

2 and 3

Step-by-step explanation:

Given:

a - first term, d - common difference Sum of the first 4 terms: S₁₋₄ = 30 Sum of the last 4 terms: S₄₋₇ = 66

S₁₋₄ = 4/2 (2a+3d) = 4a+6d = 30

⇒ 2a+3d=15

S₄₋₇ = S₇ - S₃ = 7/2 (2a+6d) - 3/2 (2a+2d) = 7a+21d - 3a - 3d = 4a+18d=66

⇒ 2a+9d = 33

Comparing the 2 equations:

2a+3d = 15 2a+9d = 33 9d-3d = 33-15 6d = 18 d=3 2a+3*3=15 2a = 6 a=2