Question

The sum of first 9 terms ap ap is 171 and that for first 24 terms is 996 find first term and common difference

Answer 1

Given,
S9=171
S24=996
Sn=n/2(2a+(n-1)d)
S9=9/2(2a+(9-1)d)
171=9/2(2a+8d)
171=9(a+4d)
a+4d=19-------(1)
Similarly,
S24=12(2a+23d)
276=12(2a+23d)
2a+23d=23---------(2)
From equation (1) and (2), we get
d= -1 and a=23

Answer 2

Given:

The sum of first 9 terms ap is 171 and that for first 24 terms is 996.

To Find:

First term and common difference?

Step-by-step explanation:

• Since we have Sum of 9 terms of AP is 171

• we can write $S_9$=171

            $S_n=\frac{n}{2} (2a+(n-1)d)\\\textrm{for n=9}\\\\S_9=\frac{9}{2} (2a+(9-1)d)\\\\S_n=171{ =\frac{9}{2} (2a+(9-1)d)$

           $\frac{171\times2}{19} =2a+8d\\\\38=2a+8d----------(1)$

• Thus also we have sum of 24 terms of AP is 996

                  $\bf S_n=\frac{n}{2} (2a+(n-1)d)\\\textrm{for n=24}\\\\S_2_4=\frac{24}{2} (2a+(24-1)d)\\\\S_n=996{ =\frac{24}{2} (2a+(24-1)d)$

                 $\frac{996\times2}{24} =2a+23d\\\\23=2a+23d----------(2)$

   on solving equation we get

    d=-1 and a=23

Thus, First term is 23 and common difference is -1