Question

Find the seventh term of the sequence 40, 0.4, 0.004, ....

a.
4x10^-7
b.
0.00004
c.
4x10^-9
d.
4x 10^-11


Please select the best answer from the choices provided

a) A
b) B
c) C
d) D

Answer 1

Answer: Option d. 4×
`10^(-11)`

Explanation:

In any sequence where ratio of the terms is given we always use the formula

A(n) = A(1)
`r^(n-1)`

Here A(n) is the term n

A(1) is the first term

n= number of trms

and r = ration of the terms

Here the given sequence is 40,0.4,0.004........

So A(1) = 40

Ratio 'r' of second and first term is =0.4/40=1/100

We have to find 7th term so n=7

Now we put the values in the formula

A(7) =
`40(1/100)^(7-1)`

=
`40(1/100)^(6)`

=
`40/100^(6) =40/10^(12)`

= 40×
`10^(-12)`

= 4×
`10^(-11)`