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Question

If r=nr=1r4+r2+1r4+r=67526, then n is equal to

A
10
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B
15
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C
25
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D
30
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Solution

The correct option is D 25
tr=(r4+r)+(r2r+1)(r4+r)=1+r2r+1r(r+1)(r2r+1)=1+1r(r+1)=1+(1r1r+1)
Thus, the terms are:
r=1:1+(1112)
r=2:1+(1213)
r=3:1+(1314)
...
r=n:1+(1n1n+1)
Hence, the sum: S=n+(111n+1)=n(n+2)n+1
Thus: n(n+2)n+1=67526=>n=25
Hence, (c) is correct.

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