There is a certain sequence of positive real numbers. Beginning from the third term, each term of the sequence is the sum of all the previous terms. The seventh term is equal to `1000` and the first term is equal to `1`. The second term of this sequence is equal to

Options

A. `246`
B. `(123)/(2)`
C. `(123)/(4)`
D. `124`

Answer

B

Explanation

`(b)` Sequence is `t_(1)+t_(2)+t_(3)+t_(4)+…`
`t_(3)=t_(1)+t_(2)`, `t_(7)=1000`
`t_(1)=1`
but `t_(7)=t_(1)+t_(2)+t_(3)+t_(4)+t_(5)+t_(6)`
`1000=2(t_(1)+t_(2)+t_(3)+t_(4)+t_(5))`
`=4(t_(1)+t_(2)+t_(3)+t_(4))`
`=8(t_(1)+t_(2)+t_(3))`
`=16(t_(1)+t_(2))`
`:.t_(1)+t_(2)=125//2`
`:. t_(2)=125//2-1=123//2`