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The sum of first n terms of an AP is given by Sn=2n2+3n find sixteenth term of the AP

Posted by Sourav Choudhary 8 years, 4 months ago

CBSE > Class 09 > Mathematics

1 answers

Mohit Sharma 8 years, 2 months ago

Solution:
Let an be the nth term & Sn be the sum of first n terms.

Given:
Sn = 2n²+3n

an = S(n) - S(n-1)

=2n²+3n -[ 2(n-1)²+3(n-1)]

= 2n²+3n -[2(n²+1-2n)+3n -3]

= 2n²+3n -[2n²+2-4n + 3n -3]

= 2n²+3n -2n²+4n-3n -2+3

= 2n²+2n²+3n -3n +4n -2+3

= 4n +1

an = 4n+1

a16= 4×16 +1= 64+1= 65

Hence, the 16th term of an AP is 65

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