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Every question that asks you to continue a number series, split a payment into equal instalments, or work out how a population grows is really asking about a progression — a list of numbers built by one fixed rule.
Only two rules are worth knowing. In an arithmetic progression (AP) you keep adding the same number: 5, 9, 13, 17 — add 4 each time. In a geometric progression (GP) you keep multiplying by the same number: 3, 6, 12, 24 — multiply by 2 each time.
That single distinction — add versus multiply — decides every formula you will use. Six formulas cover the entire chapter: the nth term and the sum for an AP, the nth term and the sum for a GP, the sum of an infinite GP, and the two means. Learn those six and you never have to write a series out term by term again.
1. The 13th term of the arithmetic progression 7, 11, 15, 19, … is:
2. The sum of the first 20 terms of the arithmetic progression 5, 9, 13, … is:
3. The sum of all two-digit numbers divisible by 7 is:
4. The 6th term of the geometric progression 3, 6, 12, 24, … is:
5. The sum of the infinite series 1 + 1/2 + 1/4 + 1/8 + … is:
6. If A is the arithmetic mean and G the geometric mean of 8 and 18, then A − G equals:
7. How many terms are there in the arithmetic progression 6, 11, 16, …, 101?
8. In an arithmetic progression the 4th term is 14 and the 9th term is 34. The common difference is: