What is the next number in the series 2, 1, (frac{1}{2}), (frac{1}{4})…
-
A.
(frac{1}{3}) -
B.
(frac{2}{8}) -
C.
(frac{3}{7}) -
D.
(frac{1}{8})
Correct Answer: Option D
Explanation
2, 1, (frac{1}{2}), (frac{1}{4})…..
There are 4 terms in the series
Therefore the next number will be the 5th term
Tn = ar(^{n − 1}) (formular for geometric series)
a = first term = 2
r = common rate = (frac{text{next term}}{text{previous term}}) = (frac{1}{2})
n = number of terms
T5 = 5th term = ?
T5 = ar(^{5 – 1})
= ar(^4)
= 2 × (ar(^{n − 1}))4
= 2 × (frac{1}{16})
= (frac{1}{8})
There is an explanation video available below.