Question

The sum of 8th and 17th term of an A. P is 36.find the sum of first 24 terms.

Answer 1

sn=n/2[2a+(n-1)d]
an=a+(n-1)d
a8=a+7d----------------1
a17=a+16d-------------2
a8+a17=36
a+7d+a+16d=36
2a+23d=36----------------3
s24

Answer 2

Answer:

432

Step-by-step explanation:

Formula of nth term : $a_n=a+(n-1)d$

So, 8th term  : $a_8=a+(8-1)d$

                        $a_8=a+7d$

So, 17th term  : $a_17=a+(17-1)d$

                        $a_16=a+16d$

Now, we are given that The sum of 8th and 17th term of an A. P is 36.

⇒$a_8+a_17 = 36$

⇒$a+7d+a+16d= 36$

⇒$2a+23d= 36$   --1

Now Formula of sum of nth term : $S_n=\frac{n}{2}(2a+(n-1)d)$

So, sum of 24 terms = $S_24=\frac{24}{2}(2a+(24-1)d)$

$S_24=12(2a+23d)$

Using 1

$S_24=12\times 36$

$S_24=432$

Hence the sum of first 24 terms is 432 .