Question 31
If the square of the 7th term of an arithmetic progression with positive common difference equals the product of the 3rd and 17th terms, then the ratio of the first term to the common difference is
Solution
The seventh term of an AP = a + 6d. Third term will be a + 2d and second term will be a + 16d. We are given that
$$ (a + 6d)^2 = (a + 2d)(a + 16d)$$
=> $$ a^2 $$ + $$36d^2$$ + 12ad = $$ a^2 + 18ad + 32d^2 $$
=> $$4d^2 = 6ad$$
=> $$ d:a = 3:2$$
We have been asked about a:d. Hence, it would be 2:3
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