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the term of three terms in an arithmetic series is 24.if 1,6and 18 are added to them respectively the results are un geometrical series ,find the term.

Sagot :

Answer:

Terms are 6, 8, 10 and 27, 8, -11

Step-by-step explanation:

Let the terms of AP be,

a,a+d,a+2d

Sum of three terms in AS is 24

S₃= a+a+d+a+2d= 3a+3d = 24

a+d = 8 —-(1)

When 1, 6, and 18 are added to them, the terms become

a+1, a+d+6=14, a+2d+18 = 26+d

If they are in GP, then the ratios of two consecutive terms should be same.

(26+d)/14 = 14 /(a+1)

(26+d)/14 = 14 /[(8-d)+1]

d²+17d-38 =0

d²+19d-2d-38 =0

d(d+19)-2(d+19)=0

d+19= or d-2 =0

d=-19 or d =2

Case 1: d=-19

a= 8-(-19) = 27

Terms are 27, 8, -11

Verification:

27+1= 28 ; 8+6=14 ; -11+18 = 7

7/14 =14/28 =1/2; Hence they ae in GP

Case 2: d=2

a = 8–2 =6

Terms are 6, 8, 10

Verification:

6+1= 7 ; 8+6=14 ; 10+18 =28

28/14 =14/7 =2 ; Hence they ae in GP

Ans: Terms are 6, 8, 10 and 27, 8, -11

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