I need some help with algebra I'm not sure how to get to the answer.
Find the number of terms in each sequence.
1. a1=4 an=42 d=2
2. a1--0.3 an=-36 d=2.1
3. 1/12, 1/8, 1/6, 5/24, 1/4,......9/8
Evaluate each sum.
1. There is an e like symbol that has a 15 on top on the bottom n=4 and to the right (3-5n)
since An = A1 + (n-1)d,
42 = 4+(n-1)*2
n=20
So, A20 = 42
This must have a typo, since you can't get to -36 with a positive difference between terms. Assuming you meant d = -2.1,
-36 = -.3 + (n-1)(-2.1)
A18 = -36
Apparently d = 1/24
9/8 = 1/12 + (n-1)(1/12)
A26 = 9/8
15
∑ (3-5n)
4
This just means to add up all the values, substituting in n=4,5,6,...,15
That means add up the sum
-17 + -22 + ... + -72
Thank you this was very helpful!
To find the number of terms in a sequence, you need to use the formula:
Number of terms (n) = (Last term (an) - First term (a1)) / Common difference (d) + 1
Let's apply this formula to solve each of the problems:
1. For this arithmetic sequence, we are given a1 (first term) = 4, an (last term) = 42, and d (common difference) = 2.
Number of terms (n) = (42 - 4) / 2 + 1
= 38 / 2 + 1
= 19 + 1
= 20
Therefore, there are 20 terms in this sequence.
2. For this arithmetic sequence, we are given a1 = -0.3, an = -36, and d = 2.1.
Number of terms (n) = (-36 - (-0.3)) / 2.1 + 1
= -35.7 / 2.1 + 1
= -17 + 1
= -16
Since the number of terms should be a positive whole number, it seems there is an issue with the values given. Please double-check the information provided or confirm if there was an error in transcription.
3. For this sequence, we are given the pattern: 1/12, 1/8, 1/6, 5/24, 1/4, .... We need to determine the number of terms.
Counting the terms in the given pattern, we have:
1st term = 1/12
2nd term = 1/8
3rd term = 1/6
4th term = 5/24
5th term = 1/4
Thus, we have 5 terms in this sequence.
Moving on to the evaluation of sums:
1. For this sum with the sigma symbol (∑), we have:
∑ (15 / (3 - 5n)), where n = 4.
To evaluate this sum, substitute n = 4 into the expression:
∑ (15 / (3 - 5n)) = ∑ (15 / (3 - 5(4))) = ∑ (15 / (3 - 20)) = ∑(15 / (-17)) = 15 / (-17)
Therefore, the sum ∑ (15 / (3 - 5n)), with n = 4, evaluates to -15/17.
If you have any other questions, feel free to ask!