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Question

# How many terms of the A.P 1, 4, 7,... are needed to give the sum 925?

A
20
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B
22
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C
24
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D
25
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Solution

## The correct option is D 25Let n = 24, then T24=1+23×3=70∴S24=(1+702)×24=71×12=852∴S24=852<925, Thus it is obvious that n must be greater than 24, which gives us n = 25, as per the choices given. ∴S25 = (a+T252)×25 because T25=T24+d=73 = 1+732×25=925 Hence (d) is correct. Alternatively: Sn=925=n2[2×1+(n−1)3]⇒1850=2n+3n2−3n⇒3n2−n−1850=0⇒3n2−75n+74n−1850=0⇒3n(n−25)+74(n−25)=0⇒n=25 or n=−743 The only admissible value of n = 25 Since number of terms cannot be negative and as a fraction too. Hence (d).

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