Question

The sum of first 5 terms of an ap is 55 and sum of first 10 terms of the ap is 235 , find the sum of first 20 terms

Answer 1

960 is the sum of first 20 terms....

Answer 2

Answer-

The sum of first 20 terms is 970

Solution-

We know that, sum of n numbers in AP is,

$\sum_{k=1}^{n-1}{(a+kd)}=\frac{n}{2}(2a+(n-1)d)$

Where,

a = first term,

d = common difference

Here, it is given that, the sum of first 5 terms is 55 and sum of first 10 terms is 235

Putting it in the formula,

$\Rightarrow \frac{5}{2}{(2a+(5-1)d)}=55,\ and\ \frac{10}{2}{(2a+(10-1)d)}=235$

$\Rightarrow {(2a+4d)}=\frac{55\times 2}{5},\ and\ {(2a+9d)}= \frac{235}{5}$

$\Rightarrow {(2a+4d)}=22,\ and\ {(2a+9d)}= 47$

Solving these equation we get,

$\Rightarrow a=1,\ d=5$

Now, we have to calculate the sum of 20 terms,

So,

$\sum_{k=1}^{19}{(a+kd)}=\frac{20}{2}(2(1)+(20-1)(5))=10(2+95)=10\times 97=970$