Question

find 4 consequetive terms in an AP, whose sum is 20 and sum of whose square is 120​

Answer 1

Answer:

2,4,6,8

Step-by-step explanation:

Let a-3d, a-d, a+d, a+3d are the four terms in A.P

(a-3d)+(a-d)+(a+d)+(a+3d)=20 (Given)

4a=20

a=5

(a-3d)²+(a-d)²+(a+d)²+(a-3d)²=120 (Given)

(a²+9d²-6ad)+(a²+d²-2ad)+(a²+d²+2ad)+(a²+9d²+6ad)=120

4a²+20d²=120

4×(5)²+20d²=120 (Putting value of a)

100+20d²=120

20d²=20

d²=1

d=±1

a-3d = 5-(3×1)=2

a-d = 5-1=4

a+d = 5+1=6

a+3d = 5+(3×1)=8

Terms are 2,4,6,8

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