Question

Matchsticks are used to make a sequence of

patterns:
3 , 5 , 7 ...

Find the nth term rule for the number of
matchsticks in pattern n

Answer 1

Tn = 1 + 2n

Explanation:

Given the arithmetic sequence

3 , 5 , 7 ...

The nth term of an AP is expressed as;

Tn = a + (n-1)d

a is the first term = 3

d is the common difference = 5-3 = 7-5 = 2

n is the number of terms

Substitute

Tn = 3 + (n-1)(2)

Tn = 3 + 2n-2

Tn = 1 + 2n

Hence the nth term rule for the number of matchsticks in pattern n is 1 + 2n