Arithmetic Sequence

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I need help on this question on arithmetic sequences because I don’t understand how to solve it. Help would be appreciated ^^
 

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Subhotosh Khan

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Please help I don’t understand this problem!

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What have you learned about arithmetic sequence?

If 'a' is the first number of the sequence and 'd' is the common difference -​
do you know the expression for common 'n' th element of the sequence?​
do you know the expression for the sum of the consecutive elements from term 'm' to 'n' (m>n)?​
 
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What have you learned about arithmetic sequence?
Not much, but normally I can solve a question given the terms but this question doesn’t give terms in the sequence so I am not really sure the steps in solving this. Normally I would find the pattern and then apply it to any numbers I need to find but this isn’t the case.
 

topsquark

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Not much, but normally I can solve a question given the terms but this question doesn’t give terms in the sequence so I am not really sure the steps in solving this. Normally I would find the pattern and then apply it to any numbers I need to find but this isn’t the case.
Start here:

[math]a_n = a_0 + nd[/math]
What is [math]a_0 + a_1 + \text{ ... }[/math] in terms of [math]a_0[/math] and d?

What is [math]a_{20} + a_{21} + a_{22}[/math] in terms of [math]a_0[/math] and d?

-Dan
 

pka

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In the first question an Arithmetic progression (AP) is [MATH]a_n=a_1+(k-1)d[/MATH] where [MATH]a_1[/MATH] is a positive integer and [MATH]d[/MATH] is the common difference. The sum of of the first [MATH]n[/MATH] terms is [MATH]\sum\limits_{k = 0}^{n - 1} {\left( {{a_1} + kd} \right)} = \frac{{n({a_1} + {a_n})}}{2}[/MATH]
 
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I’m sorry, but I’m only an year 7 so I don’t really understand all these symbols. Sorry once again if it takes too much time to explain. Sorry
 

Subhotosh Khan

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If 'a' is the first number of the sequence and 'd' is the common difference -do you know the expression for 'n' th element of the sequence?
Do you know the answer of the question posed above?

We are trying to figure out the first step of the explanation - so that it will make sense to you.
 
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topsquark

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I’m sorry, but I’m only an year 7 so I don’t really understand all these symbols. Sorry once again if it takes too much time to explain. Sorry
If you don't understand a the level of what they are asking then why have you been asked the question?

The sum of the first 10 terms in the sequence:
[math](a_0) + (a_0 + d) + (a_0 + 2d) + \text{ ... } + (a_0 + 9d)[/math] is what? Write it out and combine like terms.

-Dan
 

Dr.Peterson

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Which problem are you doing? I suppose you must mean #5,
1626035990255.png

And what help do you need?

We need at least to know what tools you have available. What have you learned about arithmetic progressions, and possibly about number theory? What did you try, and what happened?

I would write an equation using whatever formulas you have learned for the sum of such a progression, which will have two variables. Solve as much as you can, and apply the results to the question asked. I haven't tried it yet, since I don't know what you are have available.

I’m sorry, but I’m only an year 7 so I don’t really understand all these symbols. Sorry once again if it takes too much time to explain. Sorry
So, what symbols do you understand? That's why you need to show us what you have learned.
 
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Joined
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If you don't understand a the level of what they are asking then why have you been asked the question?

The sum of the first 10 terms in the sequence:
[math](a_0) + (a_0 + d) + (a_0 + 2d) + \text{ ... } + (a_0 + 9d)[/math] is what? Write it out and combine like terms.

-Dan
Would it be 10a0+ 45?
 
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Jomo

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The first sentence gives you the following equation.

Let a = 1st term.
(a)+(a+d)+(a+2d)+ ... +(a+9d) = (a+19d) + (a+20d) + (a+21d)
 
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