High School

The sum of the first four terms of an arithmetic progression (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 :

Answer:

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

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