Question

9. In an A.P. if the 12th term is - 13 and the sum of its
first four terms is 24, find the sum of its first 10 terms.
​

Answer 1

Step-by-step explanation:

12

th

term of the A.P is −13

sum of firts four terms is 24

Let, the 1st term of the A.P is a.

and common difference of the A.P is d.

We know, the formula for nth of an A.P. is ,

t

n

=a+(n−1)d

and, the formula for the sum of n−terms of an A.P. is,

S

n

=

2

n

[2a+(n−1)d]

By the question,

t

12

⇒a+(12−1)d=−13

⇒a+11d=−13

⇒a=−13−11d------(i)

S

4

→

2

4

[2a+(4−1)d]=24

⇒2a+3d=12

⇒a=

2

12−3d

------(ii)

comparing (i) and (ii) we get,

−13−11d=

2

12−3d

⇒−22d+3d=26+12

⇒−19d=38 ⇒d=−2

Now, from (i) we get,

a=−13+22

⇒a=9

Hence, sum of the first 10 terms, is,

S

10

=

2

10

[18+(10−1).(−2)]

=5[18−18]=0

i hope it's helpful for you ☺️