17. The sum of the first and 8 terms and first 24 terms of an AP are equal. Findthe sum of its 32 terms.​

Q- The sum of first 8 terms and first 24 terms of an A.P. are equal . Find the sum of first 32 terms .

• In these type of Questions , we Simply derive relation between first term(a) and common Difference (d) .

• In this question , we will compare 8th and 24th term .

• Then we will get a relation between a and d .

• Then we will use that relation , to find the sum of first 32 terms .

• 
• It's an A.P.

• a = first term .
• d = common difference
• 

Since , we know that the sum of first 8 terms is equal to the sum of first 24 terms

so ,

equating them ..

Now ,

We have to find the sum of first 32 terms ..

so , using the Formula

From eq(i) ,

• 2a + 31d = 0

So , the sum of first 32 terms would be 0 .

Where ,