Find the nth term of sequences with this Corbett Maths worksheet, including examples and a QR code for video tutorials.

The image contains two questions asking to find the nth term for various sequences. Here are the solutions:

Question 1:
(a) 5, 8, 11, 14, ...
This is an arithmetic sequence with first term a = 5 and common difference d = 3.
nth term: a + (n-1)d = 5 + (n-1)3 = 3n + 2

(b) 9, 14, 19, 24, ...
This is an arithmetic sequence with a = 9, d = 5.
nth term: 9 + (n-1)5 = 5n + 4

(c) 1, 3, 5, 7, ...
This is an arithmetic sequence with a = 1, d = 2.
nth term: 1 + (n-1)2 = 2n - 1

(d) 10, 14, 18, 22, ...
This is an arithmetic sequence with a = 10, d = 4.
nth term: 10 + (n-1)4 = 4n + 6

(e) 2, 7, 12, 17, ...
This is an arithmetic sequence with a = 2, d = 5.
nth term: 2 + (n-1)5 = 5n - 3

(f) 3, 9, 15, 21, ...
This is an arithmetic sequence with a = 3, d = 6.
nth term: 3 + (n-1)6 = 6n - 3

(g) 11, 31, 51, 71, ...
This is an arithmetic sequence with a = 11, d = 20.
nth term: 11 + (n-1)20 = 20n - 9

(h) 20, 23, 26, 29, ...
This is an arithmetic sequence with a = 20, d = 3.
nth term: 20 + (n-1)3 = 3n + 17

(i) 1, 7, 13, 19, ...
This is an arithmetic sequence with a = 1, d = 6.
nth term: 1 + (n-1)6 = 6n - 5

(j) 100, 125, 150, 175, ...
This is an arithmetic sequence with a = 100, d = 25.
nth term: 100 + (n-1)25 = 25n + 75

(k) 13, 22, 31, 40, ...
This is an arithmetic sequence with a = 13, d = 9.
nth term: 13 + (n-1)9 = 9n + 4

(l) 1.5, 2, 2.5, 3, ...
This is an arithmetic sequence with a = 1.5, d = 0.5.
nth term: 1.5 + (n-1)0.5 = 0.5n + 1

Question 2:
(a) 10, 7, 4, 1, ...
This is an arithmetic sequence with a = 10, d = -3.
nth term: 10 + (n-1)(-3) = -3n + 13

(b) 6, 4, 2, 0, ...
This is an arithmetic sequence with a = 6, d = -2.
nth term: 6 + (n-1)(-2) = -2n + 8

(c) 9, 4, -1, -6, ...
This is an arithmetic sequence with a = 9, d = -5.
nth term: 9 + (n-1)(-5) = -5n + 14

(d) 20, 10, 0, -10, ...
This is an arithmetic sequence with a = 20, d = -10.
nth term: 20 + (n-1)(-10) = -10n + 30

(e) 5, -1, -7, -13, ...
This is an arithmetic sequence with a = 5, d = -6.
nth term: 5 + (n-1)(-6) = -6n + 11

(f) 5, 4, 3, 2, ...
This is an arithmetic sequence with a = 5, d = -1.
nth term: 5 + (n-1)(-1) = -n + 6

(g) -6, -13, -20, -27, ...
This is an arithmetic sequence with a = -6, d = -7.
nth term: -6 + (n-1)(-7) = -7n + 1

(h) -10, -13, -16, -19, ...
This is an arithmetic sequence with a = -10, d = -3.
nth term: -10 + (n-1)(-3) = -3n - 7

(i) 2.5, 2, 1.5, 1, ...
This is an arithmetic sequence with a = 2.5, d = -0.5.
nth term: 2.5 + (n-1)(-0.5) = -0.5n + 3