SOLUTION: Please help! This is my last question and I have to get it done! Thank you :) Consider the following: 4 + 8 + 12 + 16 + ... a) If tn(please see note at bottom) = 256, what

Question 314405: Please help! This is my last question and I have to get it done!
Thank you :)
Consider the following: 4 + 8 + 12 + 16 + ...
a) If tn(please see note at bottom) = 256, what is n?
b) Find the sum of 4 + 8 + 12 + 16 + ... + 256.
Note: On my paper the "t" is normal and the "n" is tiny and looks like an exponent except it is down low instead of up high. I'm not sure what this means (I dont remember learning about it) but I felt it important to tell you. And thanks again for the help!
Answer by Jstrasner(112) (Show Source): You can put this solution on YOUR website!
Hey,
First of all, this is an arithmetic sequence. The tn thing means the specific number in the sequence. Each specific number in an arithmetic sequence is:
t(n)=a(first term)+(n-1)d(the difference)
The (a) in this case is 4
The (d) in this case is also 4, the common difference between the terms
so, if t(n)=256, then:
a) 256=4+(n-1)4 => 252=(n-1)4 => 63=n-1 => n=64
b) The sum for an arithmetic sequence is S(n)= (n/2)(a1+a(n))
therefore:
S(64)=(64/2)(4+256)=8320
I hope this helps!
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