The sum of three term of an A.P is 21 & the product of the first & the third term exceeds the second term by 6, find three term ?
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let the three terms in A.P be a - d,a, a + d
where d is the common difference
given that sum of the three terms is 21 so a - d + a + a + d= 21
⇒3a = 21 ⇒ a = 7
now given (a - d)(a + d) = a + 6
⇒ a² - d² = a + 6
⇒ 7² - d ² = 13
⇒d = + 6, - 6
so third term(a + d) if +6 is taken is 13 and if - 6 is taken is 1
where d is the common difference
given that sum of the three terms is 21 so a - d + a + a + d= 21
⇒3a = 21 ⇒ a = 7
now given (a - d)(a + d) = a + 6
⇒ a² - d² = a + 6
⇒ 7² - d ² = 13
⇒d = + 6, - 6
so third term(a + d) if +6 is taken is 13 and if - 6 is taken is 1
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