Question

6. How many terms of AP 7,19,31,43,,will give sum as 3775 ?​

Answer 1

Answer:

✮  25 Terms will Give a Sum as 3775.  ✮

Step-by-step explanation:

→ Given:-

A.P. :-7,19,31,43,... , where a=7, d=12, Sₙ=3775.

→ To Find:-

  Number of terms which will give a Sum of 3775.(n)

→ Formula Applied:-

• Sₙ=$\frac{n}{2}$[2a+(n-1)d]

→ Solution:-

Sₙ=$\frac{n}{2}$[2a+(n-1)d] , where a=7, d=12, Sₙ=3775.

$\implies 3775=\frac{n}{2}[2(7)+(n-1)12]$

$\implies 3775=\frac{n}{2}\times2(7+6n-6)$

$\implies 3775=n(6n+1)$

$\implies 6n^2+n-3775=0$

$\implies 6n^2+151n-150n-3775=0$

$\implies n(6n+151)-25(6n+151)=0$

$\implies (n-25)(6n+151)=0$

$n=25,(\frac{-151}{6})$

∵ n cannot be negative.

$\implies\large\boxed{n=25}$

∴ 25 Terms of this A.P. will make a Sum of 3775.