Find a, b and c such that the following numbers are in AP, a, 7, b, 23 and c.

Explanation

Since a, 7, b, 23 amd c are in AP.
`:. 7-a=b-7underset(I)(=23)-underset(II)(b)=c-underset(III)(23)= underset(IV)("Common") " difference" `
Talking second and third terms, we get
`b-7=23-b`
`implies 2b=30`
` :. b=15`
Talking first and second terms, we get
` " " 7-a=b-7`
`implies7-a=15-7 " " [:' b=15]`
`implies 7-a=8`
`:. a= -1`
Talking third and fourth terms, we get
`23-b=c-23`
`implies 23-15=c-23 " " [:' b=15]`
`implies 8=c-23`
`implies 8+23=cimpliesc=31`
Hence,` a= -1,b=15,c=31`