SOLUTION: 1.Write in sigma notation: 0+3+8+15+24+35+48 2. Find the 10th term of the arithmetic sequence: 3/4, 13/12,17/12,.. 3. Find the 6th term of the arithmetic sequence: a-b, a,

Question 431863: 1.Write in sigma notation:
0+3+8+15+24+35+48
2. Find the 10th term of the arithmetic sequence:
3/4, 13/12,17/12,..
3. Find the 6th term of the arithmetic sequence:
a-b, a, a+b,...
4. The common difference in an arithmetic sequence is 3. The 10th term is 23. Find the first term.
5. Insert 4 arithmetic means between 5 and 9.
Answer by htmentor(1343) (Show Source): You can put this solution on YOUR website!
1. Looking at the terms of the series, we see that the n-th term is one less than n^2. For example, the 3rd term = 8 = 3^2 - 1
So, we can write the series as:

2. The arithmetic sequence 3/4,13/12,17/12,... has a common difference of 1/3.
So we can write:
a_n = a_1 + (1/3)(n-1)
Where a_1 is the first term of the sequence
So the formula for the series becomes:
a_n = 3/4 + n/3 - 1/3 -> a_n = 5/12 + n/3
So the 10th term in the sequence is a_10 = 5/12 + 10/3 = 5/12 + 40/12 = 45/12
3. The common difference is a-(a-b) = b
So the formula for the series is:
(a-b) + (n-1)b
Putting in n=6 gives:
(a-b) + 5b = a + 4b
4. An arithmetic series is written a_n = a_1 + (n-1)d
So we have a_n = a_1 + 3(n-1)
For n=10, we have
23 = a_1 + 3(9), or 23 = a_1 + 27
Therefore a_1 = -4

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