Q.292. Arithmetical Progression.

Question 292.
Find 4 terms of an AP whose sum is 26 and the sum of their squares is 189.

Answer 292.
Let the four terms be
(a - 3d), (a - d), (a + d) and (a + 3d)
Sum = 26
=> 4a = 26
=> a = 6.5

Sum of squares = 189
=> (a - 3d)^2 + (a - d)^2 + (a + d)^2 + (a + 3d)^2 = 189
=> 4a^2 + 20d^2 = 189
=> 20d^2 = 189 - 4a^2 = 189 - 4(6.5)^2 = 20
=> d^2 = 1
=> d = 1 or - 1

=> four terms are
3.5, 5.5, 7.5, 9.5
OR
9.5, 7.5, 5.5, 3.5.

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