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Compute \(1 + 4 + 7 + \cdots + 94 + 97\)

 Sep 2, 2021
 #1
avatar+114435 
+1

This is an arithmetic progression.

 

The first number,  sometimes called 'a' or  T_1 is  1

d is the common difference,    4-1=7-4=....97-94 =  3

L is the last term = 97

 

You will need to find n (the number of terms) first

Use the formula 

\(T_n=a+(n-1)d\\ 97=1+(n-1)*3\)

you can finish solving that.

Then use the following formula to find the sum of all those n terms.

 

\(S_n=\frac{n}{2}[a+L]\)

 

There are a lot of formulas in the AP and GP topic.  You have to memorize them all.

 Sep 2, 2021
 #2
avatar+22158 
+1

This is an arithmetic series whose first term is 1, whose last term is 97, and whose common difference is 3.

 

Find the number of terms and use the formula for the sum of a finite arithmetic series to get your answer.

 Sep 2, 2021
 #3
avatar+114435 
0

I have just realized that this is a repost.

 

Next time:

Please give the address of the original thread and ask someone (me if you want) to add to or comment on the original question.

Request them to also leave a note here to say they have done so.  

Thanks.

 Sep 2, 2021
 #4
avatar+114435 
+1

Here is the original

 

https://web2.0calc.com/questions/compute_12

 

Now the original answerer can also learn from all the added responses.

 Sep 2, 2021

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