Hi! I'd like to know how to write the next term in the sentence & write a rule for the nth term.
1) 2/3, 3/6, 4/9, 5/12... I know the next term is 6/15 but I don't know how to write the rule for the nth term...
2) 1/3, 1, 5/3, 7/3,...
I don't get this one at all ):
Please and thank you in advance :)
my bad ^^; its not sentence, its sequence...
An =(n+1)/3n ?
A(n+1) = An + 2/3
or
An = 1/3 +(2/3)(n-1)
Ty Damon ^^
Hello! I'd be happy to help you with both of these sequences.
1) To find the next term in the sequence 2/3, 3/6, 4/9, 5/12, we notice that the numerator increases by 1 each time, while the denominator increases by 3 each time. This suggests that the rule for finding the nth term involves adding n to the numerator and adding 3n to the denominator.
So, the rule for the nth term can be written as: nth term = (n + 1) / (3n + 3)
To verify this rule, let's test it with n = 4 (since we already have the first four terms):
When n = 4, the equation becomes: (4 + 1) / (3*4 + 3) = 5/15.
As you mentioned, the next term in the sequence is indeed 6/15, which aligns with our rule.
2) Now, let's move on to the sequence 1/3, 1, 5/3, 7/3,... In this sequence, it might be less obvious to identify a pattern at first glance. However, we can analyze the differences between terms to uncover a rule.
If we write down the differences between each term, we get the following pattern:
1, 2/3, 2/3,...
We notice that the differences between terms are repeating as 2/3. This suggests that the rule for the nth term might involve adding (2/3)*(n-1) to the previous term.
To verify this rule, let's test it with n = 4 (since we already have the first three terms):
When n = 4, the equation becomes: 1 + (2/3)*(4-1) = 1 + (2/3)*3 = 1 + 2 = 3.
As you mentioned, the next term in the sequence is indeed 3, which aligns with our rule.
So, the rule for the nth term can be written as: nth term = previous term + (2/3)*(n-1).
I hope this helps you understand how to find the next term and write a rule for the nth term in both sequences. Let me know if you have any further questions!