The sum of first three numbers in an ap is 18.if the product of the first and third term is 5times the common difference, find the no .
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2 , 6 & 10
15 , 6 ,& -3
Step-by-step explanation:
The sum of first three numbers in an ap is 18.if the product of the first and third term is 5times the common difference, find the no .
Let say three numbers in Ap are
a-d , a , a +d
Sum of three numbers = 18
=> a -d + a + a+d = 18
=> 3a = 18
=> a = 6
AP
6-d , 6 , 6 + d
product of the first and third term is 5 times the common difference
(a-d)(a+d) = 5d
=> (6-d)(6+d) = 5d
=> 36 - d² = 5d
=> d² + 5d - 36 = 0
=> d² + 9d - 4d - 36 = 0
=> d (d+9) -4(d+9) = 0
=> (d-4)(d+9) = 0
=> d = 4 & d = -9
if d = 4
6-d , 6 , 6+d
2 , 6 , 10
if d = -9
15 , 6 , -3
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