A series is given with one number missing. Choose the correct alternative from the given options that will complete the series: 1/4, 0.65, ?, 29/20, 1.85

Introduction / Context:
This series mixes fractions and decimals but follows a very simple additive pattern. The idea is that each term is obtained by adding a fixed decimal value to the previous term. The sequence is 1/4, 0.65, ?, 29/20, 1.85, and we must express the missing term in a form consistent with the others.

Given Data / Assumptions:
- Terms: 1/4, 0.65, ?, 29/20, 1.85.- Fractions and decimals represent the same kinds of real numbers.- One middle term is missing.- The pattern appears to involve addition of a constant decimal amount.

Concept / Approach:
To analyse the pattern, it is convenient to convert all fractions to decimal form. Then we inspect the differences between consecutive terms. If we find a constant difference, we can use it to compute the missing value and then convert that value back to a simple fraction if needed.

Step-by-Step Solution:
- Convert 1/4 to decimal: 1/4 = 0.25.- The second term is 0.65.- Difference between first and second terms: 0.65 - 0.25 = 0.40.- Express 29/20 as a decimal: 29/20 = 1.45.- The fifth term is 1.85.- Difference between fourth and fifth terms: 1.85 - 1.45 = 0.40.- This shows that consecutive terms differ by 0.40.- Apply this rule to find the missing third term: 0.65 + 0.40 = 1.05.- Convert 1.05 back into a simple fraction: 1.05 = 105/100 = 21/20.- Thus, the missing term is 21/20.

Verification / Alternative check:
- Write the series entirely in decimals using the discovered pattern: 0.25, 0.65, 1.05, 1.45, 1.85.- Each step adds exactly 0.40.- Converting back to mixed fraction and decimal notations: 1/4, 0.65, 21/20, 29/20, 1.85.- The pattern holds consistently across the series.

Why Other Options Are Wrong:
- 1.1, 19/20, 1.2 and 23/20 correspond to decimal values 1.10, 0.95, 1.20 and 1.15, respectively.- None of these values are exactly 0.40 greater than 0.65 and 0.40 less than 1.45 at the same time.- Hence they do not preserve the constant difference of 0.40 between consecutive terms.

Common Pitfalls:
- Mixing up fractions and decimals without converting them can make the pattern hard to see.- Rounding errors when working with decimals may lead to an incorrect difference value.- Some candidates may try to impose a multiplicative pattern, which does not fit the consistent additive increase observed here.

Final Answer:
The series adds 0.40 at each step, so the missing term is 21/20.