Question

The nth term of a sequence is 3(n + 3).

What are the first four terms?
12
15
1
18
21

What is the 50th term?

Which is the first term to be larger than 100?
The _____ th term​

Answer 1

see explanation

Explanation:

To find the first 4 terms, substitute n = 1, 2, 3, 4 into the n th term formula

n = 1 : 3(1 + 3) = 3 × 4 = 12

n = 2 : 3(2 + 3) = 3 × 5 = 15

n = 3 : 3(3 + 3) = 3 × 6 = 18

n = 4 : 3(4 + 3) = 3 × 7 = 21

The first 4 terms are 12, 15, 18, 21

Substitute n = 50 into the n th term formula

n = 50 : 3(50 + 3) = 3 × 53 = 159 ← 50 th term

Equate n th term formula to 100, that is

3(n + 3) = 100

3n + 9 = 100 ( subtract 9 from both sides )

3n = 91 ( divide both sides by 3 )

n = 30.333...

Thus the first term to have a value larger than 100 is the 31 st term