SPI Reasoning · Free notes

Series: SPI Reasoning

Series has 5 questions in the SPI bank, all from the 2022 paper: two ask for a missing term and three for the wrong term in a row of numbers. None needs more than Class 10 arithmetic. Each is cracked by writing the differences under the row, dividing when the terms grow fast, or spotting squares with one added or taken away, and then checking the answer against every term.

The handout has every subtopic, worked example, formula and trap with answers shown. The formula sheet is the chapter’s formulas and traps alone, on one page.

Subtopic notes

Number Series
5 questions
A number series follows one rule from term to term. Find the rule from the differences, the multipliers or the squares, then use it to fill the gap or catch the wrong term.

Formula & revision sheet

3 formulas · 6 gotchas across all subtopics — the exam-eve cheat-sheet

Formulas (3)

Write the differences first · Next term from the differences $t_{n+1} = t_n + d_n$
When the terms grow fast, divide · Next term from the multiplier $t_{n+1} = t_n \times r_n$
Squares, cubes and two series in one · Square and cube rules $t_n = n^2 \pm k \qquad t_n = n^3 \pm k$

Watch out for (6)

Blaming the wrong term of two
→ Write the differences first
Not recognising the primes
→ Write the differences first
Not checking the term after the gap
→ When the terms grow fast, divide
Keeping the multiplier fixed
→ When the terms grow fast, divide
Reading an up-and-down series as one
→ Squares, cubes and two series in one
Missing a square by one
→ Squares, cubes and two series in one

Question weightage by concept

3 concepts · 5 questions — where the marks actually sit, so you know what to drill first

Number Series5 questions · 100%

Concept	Qs	Share
Write the differences first	2	40%
Squares, cubes and two series in one	2	40%
When the terms grow fast, divide	1	20%

Test yourself on a real paper

Sit a past SPI paper, timed and marked the way the exam marks it. You see your score and every answer the moment you finish. Free to start.

Sit an SPI past paper