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Find a, b and c such that the following ...

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

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Here, `a_(2)=7 and a_(4)=23`
Let the common difference of the A.P. be 'd'.
`:. a_(2)=7 rArr a+d=7 " " ...(1)`
and `a_(4)=23 rArr a+3d=23 " "...(2)`
Subtract eq (1) from eq (2)
`{:(" "a+3d=23),(underset(-)" "aunderset(-)""+d=underset(-)""7),(bar(" "2d=16" ")),():}`
`rArr d=8`
put d=8 in equation (1), we get
a+8=7
`rArr a=-1`
Now, A.P. is -1, 7, 15, 23, 31
`:. b=15 and c=31`
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