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The sum of 3rd and 7th term of an ap is 6 and product Thier 8. Find the sum of the first 16th term of the ap.

Posted by Muhammed Hanan 4 years, 6 months ago

CBSE > Class 10 > Mathematics

2 answers

Kavya Chanana 4 years, 6 months ago

76, 20

1Thank You

Annanya Gupta 4 years, 6 months ago

so using formula for n th term a_n=a+(n-1)da n =a+(n−1)d a = first term n = no. of terms d = common difference So given a + (3-1)d + a (7-1)d = 6 2a + 8d = 6 a + 4d = 3 a = 3 - 4d (a + 2d)(a + 6d) = 8 (3 - 2d)( 3 + 2d) = 8 {substituting a = 3 - 2d} 9 - 4d² = 8 d = +1/2 and - 1/2 so when d = +1/2 then a = 3 - 2 = 1 and when d = -1/2 a = 3 + 2 = 5 so using formula for S_n=\frac{n}{2}[2a+(n-1)d]S n = 2 n [2a+(n−1)d] when d = +1/2 S_n=\frac{16}{2}[2*1+(16-1)d]S n = 2 16 [2∗1+(16−1)d] S_n=76S n =76 Similarly when d = -1/2 S_n=20S n =20 Hope this helps you!.....

3Thank You

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CBSE > Class 10 > Mathematics