Reasoning practice

Number Series Questions with Answers

Number series questions give a row of numbers that follow a hidden rule and ask for the missing or next term. SSC CGL, CHSL and MTS and RRB NTPC and Group D ask them in the reasoning section, and bank prelims ask them in the quant section. The rule may be a constant gap, a repeated multiplier, squares or cubes, or two series mixed together. The main tip is to find the gaps first and then try other rules.

Rules to remember

Constant difference: each term adds the same number (4, 9, 14, 19 has a gap of 5).
Changing differences: the gaps themselves form a pattern (for example +1, +3, +5, +7, which are odd numbers).
Multiplier series: each term is the previous one times a number, possibly plus or minus a number (x2 + 1, x3 - 2).
Increasing multiplier: x1 + 1, x2 + 2, x3 + 3 and so on, where the multiplier and the added number both increase.
Squares and cubes: n squared and n cubed series, or one of them plus or minus a small number (for example 2, 5, 10, 17, 26 is n squared + 1 for n = 1 to 5).
Prime numbers: 2, 3, 5, 7, 11, 13, 17, 19, 23, 29.
Alternating series: odd-position terms follow one rule and even-position terms follow another. Split the series in two.
Fibonacci type: each term is the sum of the two terms before it (1, 2, 3, 5, 8, 13).

Worked examples

Q1. Find the next term: 4, 9, 14, 19, 24, ?

Find the differences: 9 - 4 = 5, 14 - 9 = 5, 19 - 14 = 5, 24 - 19 = 5.
The gap is a constant 5.
Next term = 24 + 5 = 29.

Answer: 29

Q2. Find the next term: 3, 7, 15, 31, 63, ?

The differences are 4, 8, 16, 32, which double each time.
Another way: each term is double the previous one plus 1. Check: 3 x 2 + 1 = 7, 7 x 2 + 1 = 15, 15 x 2 + 1 = 31, 31 x 2 + 1 = 63.
Next term = 63 x 2 + 1 = 127. Using differences: 63 + 64 = 127. Both methods agree.

Answer: 127

Q3. Find the next term: 7, 8, 18, 57, 232, ?

The gaps are 1, 10, 39, 175, with no clear pattern, so try multipliers.
7 x 1 + 1 = 8.
8 x 2 + 2 = 18.
18 x 3 + 3 = 57.
57 x 4 + 4 = 232.
The multiplier and the added number both rise by 1 each step. Next: 232 x 5 + 5 = 1165.

Answer: 1165

Shortcuts that save time

Look at the size of the jump. Slow growth points to addition or a changing gap, while fast growth points to multiplication or cubes. Picking the right family at once saves time and prevents a random guess.
If the first rule you try fits the first two gaps but fails on the third, drop it. A rule must fit every term, not just the first few, before you mark an answer.
Use the options. Test each option against the pattern instead of finding the next term from scratch, and skip the question if no option fits cleanly, since a wrong answer costs marks.

Where this appears

SSC CGL Tier-1	General Intelligence & Reasoning section
SSC CHSL Tier-1	General Intelligence section
SSC MTS	Reasoning section
RRB NTPC CBT-1	General Intelligence & Reasoning section
IBPS PO Prelims	Quantitative Aptitude section

Number Series

Practice Set

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Find the next term: 58, 69, 63, 74, 68, ?

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