Question

in the AP 7,14,21... how many terms are to be considered for getting sum 5740.

Answer 1

Answer:

We have to consider 40 terms to get the sum 5740

Step-by-step explanation:

$\text{Given A.P is 7, 14, 21.......}$

$\text{Here, a=7 and d=7}$

$\textbf{Given: }S_n=5740$

$\frac{n}{2}[2a+(n-1)d]=5740$

$\frac{n}{2}[2(7)+(n-1)(7)]=5740$

$\implies\,n[14+7n-7]=2{\times}5740$

$\implies\,n[7n+7]=11480$

$\implies\,7n^2+7n-11480=0$

$\implies\,n^2+n-1640=0$

$\implies(n+41)(n-40)=0$

$\implies\,n=40,-41$

$\text{But n cannot be negative }$

$\therefore\boxed{\bf\,n=40}$

Find more:

Find the value of x if 2 + 7 + 12 +17+...... + x = 156.

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