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Find the sum of the first 25 terms of an AP whose nth term is given by an=7-3n

Posted by Rohit Prasad 6 years, 4 months ago

CBSE > Class 10 > Mathematics

1 answers

Sia ? 6 years, 4 months ago

Given, a_n = 7 - 3n
Put n = 1, a₁ = 7 - 3 {tex}\times{/tex} 1 = 7 - 3 = 4
Put n = 2, a₂ = 7 - 3 {tex}\times{/tex} 2 = 7 - 6 = 1
Common difference(d) = 1 - 4 = -3
S_n = {tex}\frac { n } { 2 } [ 2 a + ( n - 1 ) d ]{/tex}
S₂₅ = {tex} \frac { 25 } { 2 } [ 2 \times 4 + ( 25 - 1 ) ( - 3 ) ]{/tex}
{tex}= \frac { 25 } { 2 } [ 8 - 72 ]{/tex}
{tex}= \frac { 25 } { 2 } \times - 64{/tex}
= -800

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