Sequence and Series
Arithmetic Series Grouping
JEE Main 2020
Grade 11
Question:
If the sum of 40 terms of the series $3 + 4 + 8 + 9 + 13 + 14 + 18 + 19 + \dots$ is $102m$, then $m$ equals:
(1) $5$
(2) $10$
(3) $20$
(4) $40$
Step-by-Step Solution
Key Concept: Group consecutive pairs: $(3 + 4),(8 + 9),(13 + 14), \dots$, giving 20 pairs. The sums of pairs form an A.P. Sum that A.P.
The detailed step-by-step mathematical proof is available inside the Mathbee app workspace.
Correct Answer: (3)