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प्रश्न
The sum of three consecutive terms of an AP is 21 and the sum of the squares of these terms is 165. Find these terms
उत्तर
Let the required terms be (a-d) , a and ( a+d)
Then (a-d) + a+ (a+d) = 21
⇒ 3a = 21
⇒ a =7
Also , `(a - d)^2 + a^2 + (a + d)^2 = 165`
⇒ `3a^2 + 2d^2 = 165 `
⇒ `(3 xx 49 +2d^2) = 165`
⇒`2d^2 = 165 - 147 = 18`
⇒`d^2 = 9`
⇒ `d = +- 3`
Thus ,`a = 7 and d = +- 3`
Hence, the required terms are (4,7,10) or (10,7,4).
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