Question

the terms A B C are between 2 and 18 2,A,B form an ap and B,C,18 form a gp .if A+B+C=25 ,then find A,B,C

Answer 1

Answer:

A=5 ; B=8 ; C=12

Step-by-step explanation:

Given: 2,A,B are in A.P. ; B,C,18 are in G.P. ; A+B+C=25 --------------[1]

∵ 2,A,B are in A.P. ∴ 2A = B+2 --------------[2]

Also, B,C,18 are in G.P. ∴ C² = 18.B --------------[3]

On multiplying with 2 on both sides in equation 1, we get

2A+2B+2C = 50

⇒ B+2+2B+2C = 50                  {from 2}

or 3B+2C = 48

On multiplying with 6 on both sides in above equation, we get

18B+12C = 288

⇒ C²+12C-288 = 0                  {from 3}

or C²-12C+24C-288 = 0

or C(C-12)+24(C-12) = 0

or (C-12)(C+24) = 0

⇒ C=12 or C=-24

∵All A,B,C lies between 2 and 18. ∴ C can not be -24.

⇒ C = 12

From 3, C² = 18B

⇒ 12² = 18B

or 144 = 18B

⇒ B = 8

From 1, A+B+C = 25

⇒ A+8+12 = 25

⇒ A = 5

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