if the first term of the AP is 4and the sum of the first five terms is equal to one-fourth of the sum of the next five terms then find the fifteenth term
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Step-by-step explanation:
let the A.P. be a,a+d,a+2d.......
We have T
1
+T
2
+T
3
+T
4
+T
5
=
4
1
[T
6
+T
7
+T
8
+T
9
+T
10
]
∵ sum =
2
n
(first term + last term)
Then
2
5
(T
1
+T
5
)=
4
1
×
2
5
(T
6
+T
10
)
⇒
2
5
(a+(a+4d))=
8
5
[(a+5d)(a+9d)]
⇒2a+4d=
4
1
[2a+14d]
⇒4a+8d=a+7d
⇒d=−3a ....(a=2)
⇒d=−3×2=−6
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Answer:
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