how do I do this can any body show me how?
An arithmetic sequence begins
4, 9, 14, 19, 24, . . . .
(a) Find the common difference d for this sequence.
d =
(b) Find a formula for the nth term an of the sequence.
an =
(c) Find the 35th term of the sequence.
a35 =
the common difference is d=5
So, the nth term is 4 + 5(n-1) or, 5n-1
SORRY 35th term would be
4 + 5(35-1) = 4 + 5(34) = 4 + 170 = 174
(a) What this means is, we are trying to find one number that is added or subtracted from each term to get the next term. Since this is an arithmetic sequence, the d will always be the same. You can find d by subtracting the first term from the second term (9-4) and getting d = 5
(b) nth term formula ...
(1st term) + d(n-1)
The nth term in this sequence is 4 + 5(n-1). You can check this by plugging the # of the term in for n. The 1st term would be 4 + 5(0) = 4
(c) plug 35 into our formula to get
4 + 5(35) = 4 + 175 = 179
THANKS NICK with your help i was able to solve my problem. Appreciate it!
For the arithmetic sequence beginning with the terms {9, 14, 19, 24, 29, 34 ...}, what is the sum of the first 23 terms
D=5
9+5(N-1)
9+5 (4-5)
9+5 (23-1)= 4+5(23) = 4+207
To find the answers to the given questions, let's break down the process step by step:
(a) Find the common difference d for this sequence.
To find the common difference, you need to find the difference between any two consecutive terms in the sequence. In this case, subtract the second term from the first term:
9 - 4 = 5
Therefore, the common difference (d) for this sequence is 5.
(b) Find a formula for the nth term an of the sequence.
To find a formula for the nth term of an arithmetic sequence, you can use the formula:
an = a1 + (n - 1) * d
where:
an is the nth term of the sequence,
a1 is the first term of the sequence,
n is the position of the term you want to find,
d is the common difference of the sequence.
In this case, the first term (a1) is given as 4, and the common difference (d) is 5. Plugging these values into the formula, we have:
an = 4 + (n - 1) * 5
(c) Find the 35th term of the sequence.
To find the 35th term (a35) of the sequence, plug the value of n as 35 into the formula from step (b):
a35 = 4 + (35 - 1) * 5
= 4 + 34 * 5
= 4 + 170
= 174
Therefore, the 35th term of the sequence is 174.