Question

3, 12, 27, 64, 75, 108

a) give the next number in each pattern
b) what is the rule to find the nth term?
c) what is the 20th term?

Please help + explain! :)

Answer 1

No easy pattern can be found for the numbers you wrote.

A form can be found for these numbers:

3 , 12 , 27 , 48 , 75 , 108

n = 1

a1 = 3 = 3 • 1 = 3 • 1²

n = 2

a2 = 12 = 3 • 4 = 3 • 2²

n = 3

a3 = 27 = 3 • 9 = 3 • 3²

n = 4

a4 = 48 = 3 • 16 = 3 • 4²

n = 5

a5 = 75 = 3 • 25 = 3 • 5²

n = 6

a6 = 108 = 3 • 36 = 3 • 6²

Next term a7 = 3 • 7² = 3 • 49 = 147

n-th term:

an = 3 • n²

a20 = 3 • 20² = 3 • 400 = 1200

If you wrote the numbers incorrectly in the sequence, then this solution is correct.

But if the numbers in the sequence are really 3 , 12 , 27 , 64 , 75 , 108 then I don't know what the solution is.

Answer 2

If you meant 3, 12, 27, 48, 75, 108 then the nth term is 3*n^2
if this is correct, then the answers to the questions are simple.

Answer 3

Hi,
3, 12, 27, 64, 75, 108 is what my question paper says. I'm not sure either, although I got the answers today and it says:
the next term is 147 (b) the rule to find the nth term is 3×n² and (c) the 20th term is 1200.

Answer 4

Thank you for your help though :)