Sign in

A-Level Maths | Sequences & Series

Last updated on 

What do the letters mean?

  • n: the term e.g. n=4 means we are talking about the 4th term in the sequence
  • a: first term
  • l: last term
  • d: common difference (the difference in arithmetic sequences)
  • r: common ratio (the multiplier in geometric sequences)

Arithmetic Sequences

Arithmetic sequences: a common difference gets added to each member e.g. 10, 12, 14, 16

  • nth term: a + (n - 1)d
  • sum of first n terms: 0.5n [2a + (n - 1)d ]

Question 1

Question 2

Question 3

Question 4

Question 5

Question 6

Question 7

Question 8

Geometric Sequences

Geometric sequences: a common ratio gets multiplied to each member e.g. 10, 15, 22.5

  • nth term: arn - 1
  • sum of first n terms: a(1 - rn)/ (1-r)
  • sum of first n terms: a(rn - 1)/ (r-1)
  • sum to infinity: a/(1 - r)

Question 9

Question 10

Question 11

Question 12

Question 13

Question 14

Question 15

Question 16

Question 17

< A-Level Maths Questions by Topic