High School

The sum of the first 7 terms of an arithmetic progression (AP) is 63, and the sum of its next 7 terms is 161. Find the 28th term of this AP.

a) [tex]31[/tex]
b) [tex]33[/tex]
c) [tex]35[/tex]
d) [tex]37[/tex]

Answer :

Final answer:

The 28th term of the given arithmetic progression (AP) is 31. Therefore, the correct answer is option a) 31.

Explanation:

The 28th term of the given arithmetic progression (AP) is 31.

  1. Calculate the common difference by subtracting the sum of the first 7 terms from the sum of the next 7 terms: 161 - 63 = 98.
  2. Divide the common difference by 7 to find the value of each common difference which is 98/7 = 14.
  3. The 28th term is found by adding 14 to the last term in the 14th term: 17 + 14 = 31.

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