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the sum of the third and the seventh terms of an A.P is 6 and their product is 8 . find the sum of first sixteen terms of A.P

Posted by Hima Babu 6 years, 3 months ago

CBSE > Class 10 > Mathematics

2 answers

Sambhav Maheshwari 6 years, 3 months ago

a + 2d +a + 6d=6 2a + 8d=6 Divide by 2 a + 4d = 3 (1) (a + 2d) (a + 6d) = 8. (2) From (1) a =3-4d Put the value of a in eq(2) (3-4d +2d) (3-4d + 6d) = 8 (3-2d) (3 +2d) =8 (3)^2 - (2d)^2 =8 9 - 4d = 8 -4d= 8-9 d= 1/4 Put the value of d in eq(1) a= 3 - 4(1/4) a= 3 -1 a=2 Sn =n/2(2a + (n - 1)d) S16= 16/2(2(2) + (16 -1)1/4) S16=8(4 +15/4) =8( 16+15/4) =8(31/4) =2(31) =62 ans

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Viswajeet Sharma 6 years, 3 months ago

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