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The number of terms common between serie...

The number of terms common between series 1+2+4+8+… to 100 terms and 1+4+7+10+… to 100 terms is

A

6

B

4

C

5

D

none of these

Text Solution

Verified by Experts

The correct Answer is:
C
Soppose `m^(th)` term of first sequence be same as the `n^(th)` term of the second sequences. Then,
`2^(m-1)=1+(n-1)xx3rArr2^(m-1)=3n-2rArr2^(m-2)+1=(3n)/(2)` . . . (i)
We have, `1lem,nle100`
`:." "(3n)/(2)le150`
`rArr" "2^(m-2)+1le150`
`rArr" "2^(m-2)le149rArrm-2le7rArrnle9rArrm=1,2, . . . ,9`.
From (i), we have
`n=(2)/(3)(2^(m-2)+1)`
We observe that `n inN` for m = 1,3,5,7,9.
Hence, there are five common terms in the sequences.
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