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प्रश्न
The sum of the first three terms of an A.P. is 33. If the product of the first and the third terms exceeds the second term by 29, find the A.P.
उत्तर
Let first three terms of A.P. be a – d, a, a + d.
Given, a – d + a + a + d = 33
⇒ 3a = 33
⇒ a = 11 ...(i)
And (a – d)(a + d) = a + 29
⇒ a2 – d2 = a + 29
⇒ (11)2 – d2 = 11 + 29 ...[From equation (i)]
⇒ 121 – d2 = 40
⇒ d2 = 81
⇒ d = ± 9
When, a = 11 and d = 9
Then, A.P. is 2, 11, 20......
When, a = 11 and d = –9
Then, A.P. is 20, 11, 2......
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