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Sum of Infinite Terms

Consider an a...

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 seris are the maximum possible four digit numbers, then the number of common terms in these two series is equal to

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Solution

By observation
$A . P : 11, 16, 21, 26 \dots G . P : 4, 8, 16, 32 \dots$
So common terms are $16, 256, 4096$

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