Quantitative Aptitude :: progressions - Discussion

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Explanation:
Let 'a' be the first number of the series and 'd' be the common difference.
Then, according to the question,
=> a + (a + d ) + ( a + 2d ) = 3*(a + d) = 33.
=> a + d = 11, or second term = 11. Then, first term = 11-d.
Then, ( 11- d )^2 + 11^2 + ( 11 + d )^2 = 491.
=> 2(d^2) = 491 - ( 3 * 121).
=> 491 - 363 = 128.
=> d^2 = 64, d = 8, a = 3.
So, the numbers are 3, 11 and 19.