Sequences and Series · Class 11 · CBSE · Science Mathematics
Three numbers are in arithmetic progression. Their sum is 21 and their product is 315. Find the three numbers.
Practice question from Sequences and Series (Class 11 · CBSE · Science Mathematics), with the correct answer and a step-by-step solution.
hard · Subjective · Q-3273C6
Three numbers are in arithmetic progression. Their sum is 21 and their product is 315. Find the three numbers.
Answer: Let the three numbers be 7 - d, 7, and 7 + d, since their sum is 21. Their product gives 7(49 - d²) = 315, so d² = 4 and d = 2 in increasing order. Therefore, the numbers are 5, 7, and 9.
Solution
Let the terms be , , and . From the product, , so , which gives . Taking the increasing order, , and the numbers are .
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