If the sum of the first 40 terms of 3 + 4 + 8 + 9 + 13 + 14 + 18 + 19 + ⋯ is 102 m , then m equals:

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MathematicsSequence & SeriesA.P.Medium2 minQB

MathematicsMediumsingle choice

If the sum of the first 40 terms of $3 + 4 + 8 + 9 + 13 + 14 + 18 + 19 + \dots$ is $102 m$ , then $m$ equals:

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Answer:

Solution:

The odd-position terms form an A.P. from 3 to 98, and the even-position terms one from 4 to 99, each with 20 terms. Their total is $10 (3 + 98) + 10 (4 + 99) = 2040 = 102 \cdot 20$ .

Stream:JEESubject:MathematicsTopic:Sequence & SeriesSubtopic:A.P.

⏱ 2mℹ️ Source: QB

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