The sum of the first three terms of an AP is 33. If the product of the first and the third
tem exceeds the second term by 29, find the AP.
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a₁+a₂+a₃ = 33
a+(1-1)d + a+(2-1)d + a+(3-1)d = 33
a + a+d + a+2d = 33
3a+3d = 33
3 (a+d) = 33
∴ a+d = 11 --- (i)
a = 11-d
a₁ * a₃ = a₂ + 29
11-d * 11-d+2d = 11-d+d + 29
11-d * 11 + d = 40
{ (a-b) (a+b) }
(11)² - (d)² = 40
121 - d² = 40
d² = 121 - 40
d² = 81
∴ d = √81
= 9
replacing values in (i),
a+9 = 11
a = 11-9
∴ a=2
The required AP:
2, 2+9, 2+ 2*9, 2+ 3*9...
= 2, 11, 20, 29...
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