If the 12th term of an AP is-13 and the is sum of its first four terms is 24, what the sum of its first 10 terms?
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Answer:
Step-by-step explanation:
Given that :-
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
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