SOLUTION: ARITHMETIC SERIES - Sn=n/2(a1 + an) Find the sum of the terms of the following arithmetic sequences. 1, 4/3, 5/3, 2,..., a10 (a, sub 10) S1: an=a1 + (n-1)d [Solve for a10]

Algebra ->  Sequences-and-series -> SOLUTION: ARITHMETIC SERIES - Sn=n/2(a1 + an) Find the sum of the terms of the following arithmetic sequences. 1, 4/3, 5/3, 2,..., a10 (a, sub 10) S1: an=a1 + (n-1)d [Solve for a10]      Log On


   

Question 978199: ARITHMETIC SERIES - Sn=n/2(a1 + an)
Find the sum of the terms of the following arithmetic sequences.
1, 4/3, 5/3, 2,..., a10 (a, sub 10)

S1: an=a1 + (n-1)d [Solve for a10]
S2: s10 = n/2 (a1+an) [Solve for S10]
Answer by Edwin McCravy(20056) About Me  (Show Source):
You can put this solution on YOUR website!
ARITHMETIC SERIES - Sn=n/2(a1 + an)
Find the sum of the terms of the following arithmetic sequences.
1, 4/3, 5/3, 2,..., a10 (a, sub 10)
To find the common difference:

d%22%22=%22%22matrix%281%2C5%2C2nd%2Cterm%2C%22%22-%22%22%2C1st%2Cterm%29%22%22=%22%22matrix%281%2C5%2C3rd%2Cterm%2C%22%22-%22%22%2C2nd%2Cterm%29%22%22=%22%22matrix%281%2C5%2C4th%2Cterm%2C%22%22-%22%22%2C3rd%2Cterm%29%22%22=%22%22

d%22%22=%22%224%2F3-1%22%22=%22%224%2F3-3%2F3%22%22=%22%221%2F3
d%22%22=%22%225%2F3-4%2F3%22%22=%22%221%2F3
d%22%22=%22%222-5%2F3%22%22=%22%226%2F3-5%2F3%22%22=%22%221%2F3

a%5Bn%5D=a%5B1%5D+%2B+%28n-1%29d 

Substitute 10 for n:

a%5B10%5D=a%5B1%5D+%2B+%2810-1%29%281%2F3%29

Substitute 1 for a1 and calculate a1.

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s%5Bn%5D+=+expr%28n%2F2%29%28a%5B1%5D%2Ba%5Bn%5D%29

Substitute 10 for n:

s%5B10%5D+=+expr%2810%2F2%29%28a%5B1%5D%2Ba%5B10%5D%29

Substitute 1 for a1 and what you got in the 
first part for a10

Edwin