4
9. Find the sum of the first 16 terms of the
AP 10, 7. 4.
Answers
Answer:
The sum of first 16 terms of A.P is -200.
Step-by-step explanation:
Given : A.P 10, 7, 4, 1, ...
To find : The sum of first 16 terms ?
Solution :
A.P 10, 7, 4, 1, ...
Here, the first term is a=10a=10
The common difference is d=7-10=-3d=7−10=−3
The sum of n terms of A.P is
S_n=\frac{n}{2}[2a+(n-1)d]S
n
=
2
n
[2a+(n−1)d]
The value of n is 16.
Substitute the value,
S_{16}=\frac{16}{2}[2(10)+(16-1)(-3)]S
16
=
2
16
[2(10)+(16−1)(−3)]
S_{16}=8[20+(15)(-3)]S
16
=8[20+(15)(−3)]
S_{16}=8[20-45]S
16
=8[20−45]
S_{16}=8[-25]S
16
=8[−25]
S_{16}=-200S
16
=−200
Therefore, the sum of first 16 terms of A.P is -200.
So, option c is correct.
#Learn more
IN aAP: the sum of 3rd and 5th terms of an a.p is 38 and sum of 7th and 10th terms of an a.p is 83,find the a.p
Step-by-step explanation:
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