The Sum Of three terms of an ap is 21 and the product of first and third term exceeds the second term by 6. Find the terms
Answers
Answered by
69
Let the three terms of AP be
Given:
Also,
Putting value of d from Equation 1
a - 13 = 0
a = 13
a - 1 = 0
a = 1
Putting value of a in Equation 1
d = 7 - a
d = 7 - 1 = 6 or d = 7 - 13 = -6
If a = 1 and d = 6
Then,
If a = 13 and d = -6
Therefore, the terms are either 1, 7, 13..... or 13, 7, 1.....
Anonymous:
So nice
Answered by
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Solution
Let the AP in Form of
a - d , a and a + d
The sum of AP
a + d + a + a - d = 21
3a = 21
a = 7
The Product of 1st and 3rd term of the Ap is
(a - d)(a +d) -6 = a
(a² - d²) = a + 6 ...... Equation
a = 7
PUTTING IT IN EQUATION
49 - d² = 7 + 6
(- d²) = - 49 + 13
d² = 36
d = ± 6
So the Ap Could be ...
We have a = 7 and d = 6
= (a-6), (a) ,(a + 6)
(1 , 7, 13 ,19...)
Now taking d = -6
The AP become ...
( 13 , 7 , 1 , -5 ...)
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