The one which says:
tn = t(n-1) - 4, t0 = 7
or
tn = 7 - 4n (for n ≥ 0).
We don't see a question like that very often at all. You've said "the following ..." twice in your question. "The following ... " means "I'm about to show you the item". In your question, there are supposed to be both a list of choices AND an arithmetic sequence "following" the question, but neither one is there. We don't stand a chance!
an = a1 + d(n - 1)
If you want to ask questions about the "following", then I suggest that you make sure that there is something that is following.If you want to ask questions about the "following", then I suggest that you make sure that there is something that is following.
To find the sum of the first 28 terms of an arithmetic sequence, you need the first term (a) and the common difference (d). The formula for the sum of the first n terms (S_n) of an arithmetic sequence is S_n = n/2 * (2a + (n - 1)d). Once you have the values of a and d, plug them into the formula along with n = 28 to calculate the sum.
You didn't say the series (I prefer to use the word sequence) of even numbers are consecutive even numbers, or even more generally an arithmetic sequence. If we are not given any information about the sequence other than that each member happens to be even, there is no formula for that other than the fact that you can factor out the 2 from each member and add up the halves, then multiply by 2: 2a + 2b + 2c = 2(a + b + c). If the even numbers are an arithmetic sequence, you can use the formula for the sum of an arithmetic sequence. Similarly if they are a geometric sequence.
We don't see a question like that very often at all. You've said "the following ..." twice in your question. "The following ... " means "I'm about to show you the item". In your question, there are supposed to be both a list of choices AND an arithmetic sequence "following" the question, but neither one is there. We don't stand a chance!
12, 6, 0, -6, ...
The following formula generalizes this pattern and can be used to find ANY term in an arithmetic sequence. a'n = a'1+ (n-1)d.
Give the simple formula for the nth term of the following arithmetic sequence. Your answer will be of the form an + b.12, 16, 20, 24, 28, ...
an = a1 + d(n - 1)
The answer depends on what the explicit rule is!
If you want to ask questions about the "following", then I suggest that you make sure that there is something that is following.If you want to ask questions about the "following", then I suggest that you make sure that there is something that is following.
-7
arithmetic sequence * * * * * A recursive formula can produce arithmetic, geometric or other sequences. For example, for n = 1, 2, 3, ...: u0 = 2, un = un-1 + 5 is an arithmetic sequence. u0 = 2, un = un-1 * 5 is a geometric sequence. u0 = 0, un = un-1 + n is the sequence of triangular numbers. u0 = 0, un = un-1 + n(n+1)/2 is the sequence of perfect squares. u0 = 1, u1 = 1, un+1 = un-1 + un is the Fibonacci sequence.
To find the sum of the first 28 terms of an arithmetic sequence, you need the first term (a) and the common difference (d). The formula for the sum of the first n terms (S_n) of an arithmetic sequence is S_n = n/2 * (2a + (n - 1)d). Once you have the values of a and d, plug them into the formula along with n = 28 to calculate the sum.
You didn't say the series (I prefer to use the word sequence) of even numbers are consecutive even numbers, or even more generally an arithmetic sequence. If we are not given any information about the sequence other than that each member happens to be even, there is no formula for that other than the fact that you can factor out the 2 from each member and add up the halves, then multiply by 2: 2a + 2b + 2c = 2(a + b + c). If the even numbers are an arithmetic sequence, you can use the formula for the sum of an arithmetic sequence. Similarly if they are a geometric sequence.
This is an arithmetic sequence with the first term t1 = 1, and the common difference d = 6. So we can use the formula of finding the nth term of an arithmetic sequence, tn = t1 + (n - 1)d, to find the required 30th term. tn = t1 + (n - 1)d t30 = 1 + (30 - 1)6 = 175