What is the first 5 values of 4n²?
My example (textbook) states:
Value of 4n² : 4 16 36 64 100
I understand that 4 is squared to get to 16. But how does it get to 36. Because 16² = 256. So by that logic, from 16, it should go to 256.
Can someone also explain how my example arrives at the last two values 64 and 100. Explain please!
Thanks
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To find the first 5 values of 4n^2 we should really define what values of n we need to consider. In fact the question should have told you! Usually it would be:
n = 1,2,3,4, 5, ...
but some sequences could be:
n = 0,1,2,3, 4, ...
Going from the given answer n = 1,2,3,4. So we have:
n = 1, 4n^2 = 4*1^2 = 4
n = 2, 4n^2 = 4*2^2 = 4*4 = 16
n = 3, 4n^2 = 4*3^2 = 4*9 = 36
n = 4, 4n^2 = 4*4*2 = 4*16 = 64
n = 5, 4n^2 = 4*5^2 = 4*25 = 100
So the first four terms are: 4, 16, 36,64 and 100
If n were 0,1,2,3 then the answers would be different. This is not a frivolous comment. Sometimes in mathematics it is very useful for the first term of a sequence to correspond to n = 0 etc
If n = 1, 4n² = 4(1) = 4
If n = 2, 4n² = 4(4) = 16
If n = 3, 4n² = 4(9) = 36
If n = 4, 4n² = 4(16) = 64
If n = 5, 4n² = 4(25) = 100
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