Question

B.formulate the nth rule for finding the term.

4. Find the 40th term in the sequence 6,12,18,24
5.Find the 18th term in the sequence 10,17,24,31

Answer 1

Question 4

• nth rule: a(n) = 6n

• 40th term: a(40) = 240

Question 5

• nth rule: a(n) = 7n + 3
• 18th term : a(18) = 129

Explanation:

The nth term in an arithmetic sequence, a(n) can be found through the formula:

a(n) = a(1) + d(n-1)

where a(1)is the first term and d is the common difference

4. Find the 40th term in the sequence 6,12,18,24

Common difference, d = 6, first term a(1) = 6

a(n) = 6 + 6(n-1) = 6 + 6n - 6 = 6n;

a(n) = 6n

a(40) = 6 x 40 = 240

5.Find the 18th term in the sequence 10,17,24,31

a(1) = 10

d = 7

a(n) = 10 + 7(n-1) = 10 + 7n - 7 = 7n + 3

a(18) = 7(18) + 3 = 126 + 3 = 129