## 4. In a sequence of positive numbers, the ratio of each term to the term immediately following it is 1 to 4. What is the rati

Question

4.
In a sequence of positive numbers, the ratio of
each term to the term immediately following it is
1 to 4. What is the ratio of the 3rd term to the 6th
term in this sequence?
(A) 1 to 4
(B) 1 to 16
(C) 1 to 64
(D) 1 to 128
(E) None of the above
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1 month 2021-08-18T16:49:13+00:00 1 Answer 0 views 0

Given

a

n

= 2a

n−1

A geometric sequence is a sequence such that any element after the first is obtained by multiplying the preceding element by a constant called the common ratio which is denoted by r.

Here, r = 2.

In a G.P.,

a

n

= a

1

r

n−1

,

where,

a

n

is the n

th

term of the sequence

a

1

is the 1

st

term of the sequence

r

is the common ratio

To find the ratio of the 8

th

term to the 5

th

term,

a

8

= a

1

2

8−1

a

8

= 2

7

a

1

a

5

= a

1

2

5−1

a

5

= 2

4

a

1

Ratio of a

8

to a

5

= 2

7

a

1

: 2

4

a

1

=

16

128

: 1

= 8 : 1

Therefore, the ratio of the 8

th

term in the sequence to the 5

th

term is

8 to 1

.