Question

In an Ap, if 12th term is -13 and the sum of first 4 terms is 24, what is the sum of the first 10 terms?

Answer 1

don't know............

Answer 2

Answer:

Sum of first 10 terms is 0  

Step-by-step explanation:

$a_{12}=-13\\\\\text{Now, using the formula of nth term}\\\\\implies a_n=a+(n-1)\times d\\\\\implies a_{12}=a+(12-1)\times d\\\\\implies a+11d=-13..........(1)\\\\\text{Also, Sum of first 4 terms is 24}\\\\\implies S_n=\frac{n}{2}(2a+(n-1)\times d)\\\\\implies S_4=\frac{4}{2}(2a+(4-1)\times d)\\\\\implies 4a + 6d = 24\\\\\implies 2a + 3d = 12.......(2)$

Now, solving both the equation ((1) and equation (2)

We get, d = -2 and a = 9

So, the A.P. is 9, 7, 5, 3, 1, -1, ..........

Now, we need to find sum of first 10 terms :

$\implies S_n=\frac{n}{2}(2a+(n-1)\times d)\\\\\implies S_{10}=\frac{10}{2}(2\times 9+(10-1)\times -2)\\\\\implies S_{10}=5\times (18-18)\\\\\bf\implies S_{10}=0$

Therefore, Sum of first 10 terms is 0