What is the next number in the series 2 1 frac ... - JAMB Mathematics 2017 Question
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
\(\frac{1}{8}\)
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Correct Option: D
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})
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