Question

The sum of the third and the seventh terms of an AP is 6 and their product is 8 . Find the sum of first sixteen terms of the AP.
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Answer 1

here's the Solution....

Answer 2

Hey mate here is ur query...

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let first term of Ap is=a & common difference=d

now According to the rule

third term , a +2d

seventh term,a+6d

now sum of third & seventh term

i.e. ,2a+8d=6
or , a+4d=3-----1
or, a=3-4d-----1
.

& product of 3rd and 7th term is

now (a+2d)(a+6d)=8-----2

putting value of a from 1 to2

(3-4d+2d)*(3-4d+6d)=8

or (3-2d)*(3+2d)=8

using formula a²-b²=(a+b)(a-b)

or 9-4d²=8

or 4d²=1

or d=±½

d=½ taken

Hence. a=3-4*½

first term a=1

Hence sum of first 16 term

using sum=n*½(2a+(n-1)d)

16/2(2*1+(16-1)½)

=8*(2+15½)

=8*19*½

=76

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Hope this will help you...