Question

Consider an arithmetic series and a geometric series having four initial terms from the set {11, 8, 21, 16, 26, 32, 4}. If the last terms of these series are the maximum possible four-digit numbers, then the number of common terms in these two series is equal to ______.

पर्याय

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Answer 1

Consider an arithmetic series and a geometric series having four initial terms from the set {11, 8, 21, 16, 26, 32, 4}. If the last terms of these series are the maximum possible four-digit numbers, then the number of common terms in these two series is equal to 3.

Explanation:

Given set = {11, 8, 21, 16, 26, 32, 4}

According to the problem,

G. P.: 4, 8, 16, 32, 64, 128, 256, 512, 1024, 2048, 4096, 8192

Last term of G.P. will be 8192, given that the last term of this series is the maximum four-digit number.

Now A. P.: 11, 16, 21, 26, 31, 36, ..., 251, 256, 261, .... 4091, 4096....

From the above A.P. and G.P., Common terms will be 16, 256 and 4096 only.