Question

There are three terms in an ap if the sum of the terms is 30 and the product of the extreme terms is 75 find the second term

Answer 1

Let the three terms =a-d, a, a+d
ATQ,
(a-d) +a+(a+d) =30
=>a-d+a+a+d=30(D is canceled)
=>3a=30
=>a=30/3=10
Again ATQ,
(a-d) (a+d) =75
=>a²-d²=75
=>(10)²-d²=75
=>100-d²=75
=>100-75=d²
=>25 =d²
=>d=
$\sqrt{25}$

=>d=±5
If d=5 a-d=10-5=5
a=10
a+d=10+5=15
If d=-5.
a-d=10-(-5)=10+5=15
a=10
a+d=10+(-5)=5