Find the next term and the nth term of the sequence: 2+4, 8+4, 18+4, 32+4, 50+4,...
a) 72 + 4 and 2n2+4
b) 68 + 4 and 68n2 + 72
c) 86 + 4 and 90 + n2
what is wrong with a)?
2+4, 8+4, 18+4, 32+4, 50+4,...
= 2(1^2)+4 + 2(2^2)+4 + 2(3^2)+4 + 2(4^2)+4 + ..
so term 6 would be 2(6^2)+4 = 72+4
and the nth term is 2(n^2)+4
A quick mental check would show that neither b) nor c) produce even the first term, so they definitely wrong.
Unless they would give you three wrong choices, a) is clearly your correct choice.
omgg thank youu so much! =D xx <3<3
oops this wasn't meant to be a question =s it was meant to be a message!
what am i saying?? sorry! i thought i had responded to a question and...oh sorry. :( whats going on?
To find the next term and the nth term of a sequence, we need to look for a pattern in the sequence.
In this sequence, we can see that the first term is obtained by adding 4 to 2: 2 + 4 = 6.
The second term is obtained by adding 4 to the square of 2: (2^2) + 4 = 8 + 4 = 12.
The third term is obtained by adding 4 to the square of 3: (3^2) + 4 = 9 + 4 = 13.
The fourth term is obtained by adding 4 to the square of 4: (4^2) + 4 = 16 + 4 = 20.
From these observations, we can see that each term in the sequence is obtained by adding 4 to the square of the previous term.
So, following this pattern, the fifth term would be (5^2) + 4 = 25 + 4 = 29.
Based on this pattern, we can conclude that the next term in the sequence is 29.
Now, let's find the nth term of the sequence. We have observed that each term is obtained by adding 4 to the square of the previous term.
Therefore, we can express the nth term as a formula: n^2 + 4.
So, the nth term of the sequence is n^2 + 4.
In summary, the next term in the sequence is 29, and the nth term is n^2 + 4.
Based on the answer choices given, the correct option would be a) 72 + 4 and 2n^2 + 4.