Question
The sum of first ten terms of an A.P. is four times the sum of its first five terms. What is the ratio of first term and common difference?
Answer: Option B
:
B
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B
Let S10 be the sum of first 10 terms and S5 be the sum of first 5 terms.
The sum upto n terms of an AP of first term a and common difference d is given by
Sn=n2[2a+(n−1)d].
Given, S10=4S5.
⇒102[2a+(10−1)d]=4×52[2a+(5−1)d]
⇒102[2a+9d]=4×52[2a+4d]
⇒ 2a+9d=4a+8d
⇒ 2a=d
⇒ ad=12
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