Statement 1 `1,2,4,8,"….."` is a GP,`4,8,16,32,"…."` is a GP and `1+4,2+8,4+16,8+32,"…."` is also a GP. Statement 2 Let general term of a GP with common ratio r be `T_(k+1)` and general term of another GP with common ratio r be `T'_(k+1)`, then the series whode general term `T''_(k+1)=T_(k+1)+T'_(k+1)` is also a GP woth common ratio r.

Options

A. Statement 1 is true, Statement 2 is true, Statement 2 is a corrct explanation for Statement 1.
B. Statement 1 is true, Statement 2 is true, Statement 2 is not a correct explanation for Statement 1.
C. Statement 1 is true, Statement 2 is false.
D. Statement 1 is false, Statement 2 is true.

Answer

A

Explanation

`1,2,4,8,"…."`
Common ratio r =2
`:.T_(k+1)=1*(2)^(k+1-1)=2^(k)`
and `4,8,16,32,"…"`
Common ratio r=2
`:.T'_(k+1)=4*(2)^(k+1-1)=4*2^(k)`
Tn, `T_(k+1)+T'_(k+1)=5*(2)^(k)=T''_(k+1)`
Common ratio of `T''_(k+1)=(5*(2)^(k))/(5*2^(k-1))=2`, which is true.
Hence, Statement 1 is true, Statement 2 is true, Statement 2 is a corrct explanation for Statement 1.