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If for an arithmetic progression (AP), [tex]a_n = 3 + 5n[/tex], where [tex]n \in \mathbb{N}[/tex], then the sum of the 21st term to the 40th term of the AP is:

A. 1980
B. 4520
C. 2560
D. 3110

Answer :

Final answer:

The sum of the 21st to 40th terms of the arithmetic progression where an = 3 + 5n is calculated using the sum formula for an AP segment. The sum is found to be 3110. Therefore, Answer 3110 is correct.

Explanation:

  • The question asks for the sum of the terms from the 21st to the 40th of an arithmetic progression (AP) where the nth term is given by an = 3 + 5n. To find the sum of these terms, we can use the formula for the sum of an AP's specific terms, which is S = n/2(a1 + an), where n is the number of terms, a1 is the first term and an is the last term in the segment being summed.
  • Step 1: Identify the first and last term of the segment. For the 21st term, a21 = 3 + 5(21) = 108. For the 40th term, a40 = 3 + 5(40) = 203.
  • Step 2: Calculate the sum of the 20 terms from the 21st to the 40th term. We have 20 terms, so S = 20/2(108 + 203) = 10(311) = 3110.
  • Therefore, the sum of the 21st to 40th terms of the AP is 3110.

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