how do you find the 12th term of the sequence an= an-1+3 ( the n and n-1 are subscript) n>2 (also equal to)? I understand how to find the first six terms,but how do you use that to find the 12th . Thanks
To find the 12th term of the sequence an = an-1 + 3, where n > 2, you can use the recursive formula to generate the terms one by one. Here's the step-by-step process:
1. Start with the given information: a1 = the first term, a2 = the second term, and the recursive formula an = an-1 + 3, where n > 2.
2. Use the recursive formula to find the third term (a3): a3 = a3-1 + 3 = a2 + 3.
3. Continue using the formula to find the fourth term (a4): a4 = a4-1 + 3 = a3 + 3.
4. Repeat the process until you reach the 12th term.
To make this process easier to understand, let's calculate the first six terms of the sequence:
a1 = the first term (given)
a2 = a1 + 3
a3 = a2 + 3
a4 = a3 + 3
a5 = a4 + 3
a6 = a5 + 3
Now that we have the first six terms, we can continue the pattern to find the 12th term:
a7 = a6 + 3
a8 = a7 + 3
a9 = a8 + 3
a10 = a9 + 3
a11 = a10 + 3
a12 = a11 + 3
By following this pattern, you can calculate each term step-by-step until you find the 12th term.
To find the 12th term of the sequence given by the formula an = an-1 + 3, where n > 2, you can use the recurrence relation to generate the terms of the sequence until you reach the 12th term.
Let's start by calculating the first few terms of the sequence:
For the first term, a1, it is not explicitly given in the problem, so we cannot compute it directly. However, the formula an = an-1 + 3 still holds for a1 if we consider n-1 = 0. Therefore, we can write a1 = a0 + 3. Since n > 2, we don't have any information about the value of a0, so we need additional information to determine a1.
Now, for the second term, a2, we can use the given formula to compute it: a2 = a1 + 3.
For the third term, a3, we can again use the formula: a3 = a2 + 3.
By continuing this pattern of using the formula an = an-1 + 3, we can find the first few terms of the sequence.
Once you have calculated the first few terms, you can continue applying the formula an = an-1 + 3 to find subsequent terms until you reach the 12th term. This can be done manually or by using a spreadsheet or calculator.
Alternatively, you can notice a pattern in the sequence and use that to find the 12th term without manually calculating each term. For example, you might notice that each term is three more than the previous term, so you could infer that the 12th term would be three more than the 11th term.
In summary, to find the 12th term of the sequence an = an-1 + 3, where n > 2, you can apply the given formula repeatedly starting from the first term until you reach the 12th term, or alternatively, you can identify any patterns in the sequence to calculate the 12th term directly.
an = an-1 + 3
where a1 has to be known, I conclude that a1 = 2
I don't understand why n>2, I was expecting n>1
Ok, lets assume our terms are 2, 5, 8 ..... , each term is 3 more than the previous one
You could just grind it out and find the 12th terms , there are not too many for that.
However, I can translate this one to
an = 3n - 1 , that will produce our sequence 2, 5, ...
so a12 = 3(12) - 1 = 35