The sum of the first three numbers in an Arithmetic Progression is 18. If
the product of the first and the third term is 5 times the common
difference, find the three numbers
Answers
Answer:
it is given that the sum of first three numbers in an AP is 18. Product of the first and the third term is 5 times the common difference.
Let first three numbers in the AP are a-d, a, a+d.
Sum of these three terms is 18.
(a-d)+a+(a+d)=18(a−d)+a+(a+d)=18
3a=183a=18
Divide both sides by 3.
a=6a=6
The value of a is 6.
The product of the first and the third term is 5 times the common difference.
(a-d)(a+d)=5d(a−d)(a+d)=5d
a^2-d^2=5da
2
−d
2
=5d
6^2-d^2=5d6
2
−d
2
=5d
36-d^2=5d36−d
2
=5d
d^2+5d-36=0d
2
+5d−36=0
d^2+9d-4d-36=0d
2
+9d−4d−36=0
d(d+9)-4(d+9)=0d(d+9)−4(d+9)=0
(d-4)(d+9)=0(d−4)(d+9)=0
d=4,-9d=4,−9
If the common difference is 4, then
a-d=6-4=2a−d=6−4=2
a+d=6+4=10a+d=6+4=10
Therefore the first three terms are 2, 6 and 10.
If the common difference is -9, then
a-d=6-(-9)=15a−d=6−(−9)=15
a+d=6+(-9)=-3a+d=6+(−9)=−3
Therefore the first three terms are 15, 6 and -3.