Question

if the 21st term of an AP is 25,find the sum of first 41 terms

Answer 1

21st term =25
$a + 20d = 25.......(1)$
sum of 41 terms
$(41 \div 2)(2a + 2(41 - 1)d) \\ = (41 \div 2)(2a + 2(40)d) \\ = (41 \div 2)(2)(a + 20d) \\ = 41(a + 20d) \\ = 41(25) ....from \: (1)\\ = 1025$
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