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  4. Given a sequence of 4 numbers, first three of which are in G.P. and the last three are in A.P. with common difference 6. If first and last terms of this sequence are equal, then the last term is

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Q. Given a sequence of 4 numbers, first three of which are in G.P. and the last three are in A.P. with common difference 6. If first and last terms of this sequence are equal, then the last term is

Sequences and Series

Solution:

Let a, ar, $a^2$, a.
Now, $2 a^2=a r+a$
image
As, $a r-a r^2=6 \Rightarrow a=8$