SOLUTION: Answer the following. Please show your work. 1+14+27+...+183 Step 1: Using the formula for the sum of an arithmetic series, find the value of each of the following: a[1]=

Algebra ->  Rational-functions -> SOLUTION: Answer the following. Please show your work. 1+14+27+...+183 Step 1: Using the formula for the sum of an arithmetic series, find the value of each of the following: a[1]=       Log On


   

Question 258725: Answer the following. Please show your work.
1+14+27+...+183
Step 1: Using the formula for the sum of an arithmetic series, find the value of each of the following:
a[1]= a[2]= a[n]= and d=a[2]-a[1]=
Step 2: Find n, the number of terms in the arithmetic sequence. Use the formula a[n]=a[1]+(n-1)d

Step 3: Find the sum of the arithmetic sequence.
Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
1+14+27+...+183
d=14-1=13
d=27-14=13
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+183=1%2B%28n-1%2913
182=%28n-1%2913
14=n-1
n=15
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a1=1
a2=a1%2B13
a3=a2%2B13=a1%2B13%2B13=a1%2B2%2813%29
a4=a3%2B13=a2%2B13%2B13=a1%2B13%2B13%2B13=a1%2B3%2813%29
So then the sum from 1 to n is
Sum=n+Sum(1 to n)*13
The sum from 1 to n=n%28n-1%29%2F2
Sum=n%2Bn%28n-1%29%2A%2813%2F2%29
Since n=15,
Sum(1-15)=15%2B15%2814%2913%2F2=15%2B1365=1380.