Arithmetic progression

[anakbulan]

The nth term of an AP is given by Tn=2n+3. Find the sum of the first 20 terms after the 3rd term (help me plsss)

 

[Steven G]

We are here to help you. The problem is that you failed to state where you need help. Is it at the very beginning of the problem at the middle,... ? We do not just solve problems for students on this site but rather help them solve it by giving them hints.

Please show us you attempt and after seeing it we will know what method you want to use and then we can guide you from there.

Do you know which term numbers they want you to add up? Do you know how to find the terms?

Here is some help. T₁=2*1+3. T₂=2*2+3. T₃=2*3+3. ...
So two things are going on if you add the terms. You are adding up the numbers on the two times table (do you know how to do that?) and you are repeatedly adding the number 3 (do you know how to calculate that?)

 

[Dr.Peterson]

What have you learned about sums of arithmetic progressions? Do you know a formula or a method? We'll want to start with that.

We also need to be sure of the meaning of the question, as words like these can be misunderstood. I would take it to mean the sum of terms 4 through 23 (20 terms, starting after the 3rd).

 

[pka]

The nth term of an AP is given by Tn=2n+3. Find the sum of the first 20 terms after the 3rd term (help me plsss)

As stated the question is incomplete. Whenever asking a question about Arithmetic progression it is necessary to state what the first term is. In this case it be \(3,~5,\text{ or any other integer}\). There are authors that are amendment on this point. What does your textbook/instructor use as the first index, the most common are \(0\text{ or }1\)?

 

[Steven G]

Good point!

 

[anakbulan]

As stated the question is incomplete. Whenever asking a question about Arithmetic progression it is necessary to state what the first term is. In this case it be \(3,~5,\text{ or any other integer}\). There are authors that are amendment on this point. What does your textbook/instructor use as the first index, the most common are \(0\text{ or }1\)?

As stated the question is incomplete. Whenever asking a question about Arithmetic progression it is necessary to state what the first term is. In this case it be \(3,~5,\text{ or any other integer}\). There are authors that are amendment on this point. What does your textbook/instructor use as the first index, the most common are \(0\text{ or }1\)?

The first index will be 1

 

[anakbulan]

What have you learned about sums of arithmetic progressions? Do you know a formula or a method? We'll want to start with that.

We also need to be sure of the meaning of the question, as words like these can be misunderstood. I would take it to mean the sum of terms 4 through 23 (20 terms, starting after the 3rd).

THANK YOU SO MUCH I’VE FINALLY GOT THE ANSWER!!

 

[Harry_the_cat]

As stated the question is incomplete. Whenever asking a question about Arithmetic progression it is necessary to state what the first term is. In this case it be \(3,~5,\text{ or any other integer}\). There are authors that are amendment on this point. What does your textbook/instructor use as the first index, the most common are \(0\text{ or }1\)?

But the question states "the nth term is given by ..." which means the 1st term is when n=1.

 

[anakbulan]

But the question states "the nth term is given by ..." which means the 1st term is when n=1.

Yeap!! You’re right

 

[Steven G]

But the question states "the nth term is given by ..." which means the 1st term is when n=1.

I need to go to the read more carefully forum

 

[Steven G]

But the question states "the nth term is given by ..." which means the 1st term is when n=1.

Wait a minute please. Let's look at this example.

a₀=5, a_n= a_n-1+11, n>1

Isn't the nth term a_n = a_n-1+11? However the the 1st term is NOT a₁. Now I think that pka does have a point?

I am getting dizzy from flipping back and forth on this one.

 

[Dr.Peterson]

For your new example, perhaps. But in your example, you didn't say "the nth term is given by [MATH]a_n[/MATH]", did you? The OP did.

If the first term is [MATH]a_0[/MATH], then you can't say the nth term is [MATH]a_n[/MATH]. And if you say the nth term is [MATH]a_n[/MATH], you can't say the first term is [MATH]a_0[/MATH].