Question

In an AP if the 12th term is -13 and the sum of its first four terms is 24 find the sum of its first ten terms

Answer 1

see above attachment ✔️

Hope it helps you ❣️✔️

Answer 2

The sum of first ten numbers is zero

Step-by-step explanation:

given :

$a_1_2=-13\\S_4 = 24$

Let the first term be a and common difference be d

therefore ,

$a_1_2 = -13 \\\\-13 = a+11d \\\\a+11d = -13 ...(1)\\\\S_n = \frac{n}{2}(2a+(n-1)d)\\\\S_4 = \frac{4}{2}(2a+3d)\\\\24= 2(2a+3d)\\\\2a+3d = 12 ..(2)$

solving 1 and 2 we get

19d = -38

d= -2

put the value of d in equation 1

a= -13 -11d

a= -13 - 11 (-2)

a = 9

then sum of its first ten terms is

$S_n = \frac{n}{2}(2a+(n-1)d)\\\\S_1_0 = \frac{10}{2}(18-18)\\\\S_1_0 =5(18-18)\\\\S_1_0 =0$

hence , The sum of first ten numbers is zero

#Learn more:

If 12th term of the ap is 213 and sum of its first four term is 24. what is sum of first ten terms?

https://brainly.in/question/1784559