Series – Reasoning Ability (Mizoram TET)
Series are sequences of numbers or figures that follow a specific rule or pattern. In reasoning tests, you are asked to:
- Identify the rule.
- Predict the next term(s) or find a missing term.
- Sometimes, compute the n‑th term or the sum of the first n terms.
1. Simple Explanation
A series is a list of numbers written in a particular order.
Two common types:
| Type | Example | Rule | Formula for n‑th term |
|---|---|---|---|
| Arithmetic Series | 2, 5, 8, 11, … | Add a constant difference (d) | (a_n = a_1 + (n-1)d) |
| Geometric Series | 3, 6, 12, 24, … | Multiply by a constant ratio (r) | (a_n = a_1 \times r^{(n-1)}) |
Other series may use alternating patterns, factorials, squares, cubes, or custom rules.
2. Key Points
| Point | What to Look For |
|---|---|
| Common Differences / Ratios | Quick check for arithmetic / geometric patterns |
| Alternating Patterns | Same rule applied to odd/even positions |
| Missing Terms | Replace “?” with a variable, set up equation |
| Pattern of Operations | +, –, ×, ÷, ×2, ÷3, +2, –3, etc. |
| Use of Indices | Terms may involve (n, n^2, n^3) |
| Check for “Special” Numbers | 0, 1, 2, 3, 5, 7, 9, 11, 13 – primes, Fibonacci, etc. |
| Essay‑style Series | Words or letters, not just numbers |
Quick Checklist for Every Series Question
- Write down the given terms with their positions.
- Test for arithmetic or geometric progression.
- Look for alternation or two interleaved sub‑series.
- Try simple operations (+, –, ×, ÷) between adjacent terms.
- If a pattern isn’t obvious, try “difference of differences” or “ratio of ratios”.
- Verify the chosen rule with all given terms.
- Compute the required term or the sum.
3. Worked Example
Question:
Find the 8th term of the series:
(4, 9, 16, 25, 36, ?)
Step‑by‑Step Solution
-
List the terms with indices
n Term 1 4 2 9 3 16 4 25 5 36 6 ? -
Observe a pattern
4 = (2^2)
9 = (3^2)
16 = (4^2)
25 = (5^2)
36 = (6^2)The term at position n is ((n+1)^2).
-
Find the 8th term
For n = 8 → ((8+1)^2 = 9^2 = 81). -
Answer
81
Check
If you plug n = 1 → (2^2 = 4), matches the first term. All terms satisfy the rule.
4. Quick Revision Summary
| Concept | Quick Recall |
|---|---|
| Arithmetic Series | (a_n = a_1 + (n-1)d) |
| Geometric Series | (a_n = a_1 \times r^{(n-1)}) |
| Alternating Pattern | Separate odd & even indices, solve each sub‑series |
| Missing Term | Set up equation using the identified rule |
| Common Tricks | Difference of differences, ratio of ratios, squares/cubes, prime numbers, Fibonacci |
| Typical Questions | Find next term, find missing term, find 10th term, compute sum of first n terms |
| Time‑Saving Tip | Always try arithmetic or geometric first; if not, look for alternation or simple operations. |
Practice Tip:
Take a 5‑minute timed drill: write down 10 random series (5 arithmetic, 3 geometric, 2 special patterns) and solve them. This will sharpen pattern‑recognition skills and speed—essential for the Mizoram TET Reasoning section.