JEE Main 2022 Mathematics question
If n arithmetic means are inserted between a and 100 such that the ratio of the first mean to the last mean is 1 : 7 and a + n = 33, then the value of n is:
Answer: (3)
Solution
Let d be the common difference of a, , …, , 100. The ratio of the first mean to the last mean is (a + d)/(100 − d) = 1/7, so 7a + 8d = 100. Also 100 = a + (n + 1)d with a +
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