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Question

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

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Solution

We have
d1=a2a1=7a
d2=a3a2=b7
d3=a4a3=23b
d4=a5a4=c23
As list of numbers is in A.P.,
so d1=d2=d3=d4
Now. d2=d3
b7=23b
b+b=30
2b=30
b15
Now, d2=d1
b7=7a
157=7a
8=7a
a=78=1
Now, d4=d2
c23=b7
c=23+157=387
c=31
Hence, a=1,b=15 and c=31.

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