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Question
The sum of the first three terms of an Arithmetic Progression (A.P.) is 42 and the product of the first and third term is 52. Find the first term and the common difference.
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Solution
Let the three times terms of an A.P. be (a - d ),a, (a + d)
sum = 42 = (a - d) + a + (a + d)
42 = 3a
⇒ ` a = 42/3`
⇒ a = 14
Also , (a - d ) (a + d) = 52
⇒ ` a^2 - d^2 = 52 `
`d^2 = a^2 - 52`
` = 196 - 52 `
`d^2 = 144`
⇒ `d = +- 12`
∴ First term ` = {(a - d,=,14,+,12,=,26),(a + d,=,14,-,12,=,2):}`
∴ A.P. is 2, 14, 26 or 26,14,2
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