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! :)
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.
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.
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.