The sum of three numbers in Arithmetic Progression is 30, and the sum of their square 318.Find the numbers.

Question

Satt Academy · Accepted Answer

Let, second term = a Common difference = dFirst term will be=a-d And third term will be = a+d according to question,

a-d+a+a+d=30 ⇒3a=30 ⇒a=303 ∴a=10 So, second term = 10 First term = (10-d) and third = (10+d) According to question , 10-d2+102+10+d2=318 ⇒102-2×10×d+d2+100+102+2×10×d+d2=318 ⇒100-20d+d2+100+100+20d+d2=318 ⇒2d2+300=318 ⇒2d2=18 ∴d=9=3so, 1st term  = 10-3=7; 2nd term= 10 & 3rd term = 10+3=13 ans. the number is 7,10,13

The sum of three numbers in Arithmetic Progression is 30, and the sum of their square 318.Find the numbers.
(Series)