If the sum of first four terms of an AP is 28 and sum of the first eight terms of the same AP is 88, then sum of first 16 terms of the AP is
Answers
Answer:
304
Step-by-step explanation:
Given:
- Sum of first four terms of an A.P = 28
- Sum of first eight terms of the A.P = 88
To find:
- Sum of first 16 terms of the A.P
Formula:
Sum of n terms of an A.P =
Substituting for sum of first four terms:
------(1)
Now substituting for the sum of first eight terms:
-------(2)
(2)-(1):
4d = 22-14
4d=8
d=2
The common difference is equal to 2
Now for finding a, let us substitute d in (2):
(2a+7×2)=22
2a=22-14
2a=8
a=4
The value of first term is 4
Sum of first 16 terms of A.P :
8(38)
=304
The sum of first 16 terms of the A.P is equal to 304
If the sum of first four terms of an A.P. is 28 and sum of the first eight terms of the same A.P. is 88, then sum of first 16 terms of the A.P is
★ Given that,
★ To find,
★ Formula :
★ Let,
➡ ᴄᴀsᴇ - 1 :-
- S8 = 28
- n = 4
➡ ᴄᴀsᴇ - 2 :-
- S8 = 88
- n = 8
★ From,
Subtract equations (1) & (2). We get,
- Substitute value of d in (1).
★ Verification,
Verify whether these values are correct or not.
- Substitute values of a & d in (1), to get LHS = RHS.
LHS =
◼ Since, LHS = RHS.
◼ Hence, it was verified.
★ Now,
- We can find out the value of sum of first 16 terms of an AP.
★ More information :
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