Question

the sum of four consecutive terms in an AP is 20 and the sum of their squares is 120 find the numbers

Answer 1

нєу тнєяє ιѕ αиѕωєя !!


ι нσρє уσυ нєℓρ !!



Let the middle term is a, common difference is d,
The the first  term = a-d, succeeding term = a+d
So the three parts are a-d, a ,a+d (i)
And sum of these parts =15
Hence a-d + a + a + d =15
3a = 15
⇒a =15/3=5
Hence the terms are 5-d,5,5+d
Sum of their squares = 83
Hhence (5-d)2 +52 + (5 + d)2 =83
⇒ 25+d2-10d +25 +25 +d2+10d = 83
⇒75 +2d2 = 83
⇒2d2 = 83-75 = 8
⇒d2= 4
d = 2,-2
So the terms are 7,5,3 or 3,5,7 by putting the value of d in (i)
So the smallest part is 3.