What is the next number in the series 2, 1, $\frac{1}{2}$, $\frac{1}{4}$...

Analyze the question: We need the next term in the sequence 2, 1, 1/2, 1/4, ...

Concept: This is a geometric progression (GP), where each term is found by multiplying the previous term by a constant common ratio, r.

Solution:

Find the common ratio:

• r = 1 ÷ 2 = 1/2
• r = (1/2) ÷ 1 = 1/2
• r = (1/4) ÷ (1/2) = 1/2

The ratio is constant, so it is a GP with r = 1/2.

Next term = (1/4) × (1/2) = 1/8

Check the options:

• A. 1/3: not equal to 1/8
• B. 2/8 = 1/4: this is the previous term, not the next
• C. 3/7: no
• D. 1/8: matches

Tip: For sequences, first test the difference between terms (arithmetic progression). If the differences are not constant, test the ratio (geometric progression). Here the differences are -1, -1/2, -1/4, which are not constant, but the ratios are all 1/2. Also watch for traps like option B, where 2/8 simplifies to 1/4, a term already in the series.