SOLUTION: Find the sum of the series 1+3.5+6+8.5+......+101 Find the sum of the first 23 term of the AP 4-3-10..... An arithmetic series have 1st term as 4 and common difference as 1/2 fin

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Question 1118070: Find the sum of the series 1+3.5+6+8.5+......+101
Find the sum of the first 23 term of the AP 4-3-10.....
An arithmetic series have 1st term as 4 and common difference as 1/2 find the first 20term
Find the sum of the first 100 term
Find the sum of arithmetic series term 1common difference 3 and last term 100
Find the sum of d first 20 term of arithmetic is identical to the sum of first 22 term. If the common difference is -2 find the first term
Osakpolormario@gmail.com
Found 2 solutions by Edwin McCravy, ikleyn:
Answer by Edwin McCravy(20056)   (Show Source): You can put this solution on YOUR website!
Find the sum of the series 1+3.5+6+8.5+......+101.
Sn = (n/2)(a1 + an)

a1 = 1

But we need first to determine n.
To do that we need d:

d = 3.5-1 = 6-3.5 = 8.5-6 = 2.5

an = a1 + (n - 1)∙d

101 = a1 + (n - 1)∙2.5

Solve that and get n = 41

Sn = (n/2)(a1 + an)

S41 = (41/2)(1 + a41)

S41 = (41/2)(1 + 101)

S41 = (41/2)(102)

S41 = 2091

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Find the sum of the first 23 term of the AP 4-3-10.....
First find d:

d = -3 - 4 = -10 - (-3) = -7

Then use

Sn = (n/2)[2∙a1 + (n-1)∙d

with n = 23, a1 = 4, d = -7

An arithmetic series have 1st term as 4 and common difference as 1/2 find the first 20 terms.
Write the first term as 4 and keep adding 1/2 over and over until
you have written 20 terms. To get you started,

the 2nd term is 4 + 1/2 = 8/2 + 1/2 = 9/2,
the 3rd term is 9/2 + 1/2 = 10/2 = 5,
etc., etc.,

Edwin
Answer by ikleyn(52792)   (Show Source): You can put this solution on YOUR website!
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