Question

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​

Answer 1

2 and 3

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