Three numbers form an arithmetic sequence with common difference of #15#. If first number is increased by #3# and third number by #21#, they become in geometric sequence. What is the first number?

1 Answer
Jan 29, 2018

First number of arithmatic sequence is #3#.

Explanation:

As numbers form an arithmetic sequence with common difference #15#, let the numbers be #a,a+15# and #a+30#, where #a# is first number.

Increasing first number by #3# and third number by #21#, we get

#a+3,a+15# and #a+51#, which are in G.P. and hence

#(a+15)^2=(a+3)(a+51)#

or #a^2+30a+225=a^2+54a+153#

or #54a-30a=225-153#

or #24a=72#

i.e. #a=3#

Hence, first number of arithmati sequence is #3#.

and numbers are #3,18,33#