JAMB Mathematics 2017 Paper

Concept:The series follows a geometric progression, meaning each term is obtained by multiplying the previous term by a constant common ratio.Explanation:List the given terms: $2, 1, \frac{1}{2}, \frac{1}{4}, \dots$.Find the common ratio $r$ by dividing any term by the term immediately before it.For example, $r = \frac{1}{2} \div 1 = \frac{1}{2}$.The first term is $a = 2$.The next term requested is the fifth term, so $n = 5$.The formula for the $n$-th term of a geometric progression is $T_n = ar^{n-1}$.Substitute the known values into the formula: $T_5 = 2 \times \left(\frac{1}{2}\right)^{5-1}$.Simplify the exponent first: $5 - 1 = 4$.So $T_5 = 2 \times \left(\frac{1}{2}\right)^4$.Now evaluate the power: $\left(\frac{1}{2}\right)^4 = \frac{1}{16}$.Multiply by the first term: $T_5 = 2 \times \frac{1}{16} = \frac{2}{16}$.Reduce the fraction to its lowest terms: $\frac{2}{16} = \frac{1}{8}$.Thus the next number in the series is $\frac{1}{8}$.Answer:$\frac{1}{8}$