JEE Main 2022 · 29 Jun · Shift 2 · Mathematics Q23

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MathematicsInteger+4 / -1Question 23 of 90

Let 3, 6, 9, 12, ... upto 78 terms and 5, 9, 13, 17, ... upto 59 terms be two series. Then, the sum of the terms common to both the series is equal to ______.

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Answer and worked solution

Official answer: 2223

Common terms are multiples of 3 that are $\equiv1\pmod4$ : $9,21,33,\dots$ (step 12). The first series ends at $3\times78=234$ .

Terms up to 234. $9+12k\le234$ gives 19 terms, ending at 225: sum $\frac{19}2(9+225)=2223$ .

Answer: 2223

Topics:Arithmetic progression

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JEE Main 2022 · 29 Jun · Shift 2, Mathematics question 23