# How To Solve Arithmetic Sequence Problems

If you're behind a web filter, please make sure that the domains *.and *.are unblocked. And they wanna ask, they want us to figure out what the 100th term of this sequence is going to be. So the second term is going to be six less than the first term. So whatever term you're looking at, you subtract six one less than that many times.- [Instructor] We are asked what is the value of the 100th term in this sequence, and the first term is 15, then nine, then three, then negative three. So if we have the term, just so we have things straight, and then we have the value, and then we have the value of the term. So let's see what's happening here, if we can discern some type of pattern. Then to go from nine to three, well we subtracted six again. And then to go from three to negative three, well we, we subtracted six again. The third term is going to be 12 minus from the first term, or six subtracted twice. Let me write this down just so, notice when your first term, you have 15 and you don't subtract six at all, or you could say you subtract six zero times. This is 15, it's just we just subtracted six once, or you could say minus one times six. This is 15 minus, we're subtracting the six three times from the 15, so minus three times six.

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The second sequence isn't arithmetic because you can't apply this rule to get the terms; the numbers appear to be separated by 3, but in this case, each number is multiplied by 3, making the difference (i.e., what you'd get if you subtracted terms from each other) much more than 3.

In the first example, the constant is 3; you add 3 to each term to get the next term.

So if we had the nth term, if we just had the nth term here, what's this going to be? So if you wanna figure out the 100th term of this sequence, I didn't even have to write it in this general term, you could just look at this pattern. 594 minus 14 would be 580, and then 580 minus one more would be 579.

It's going to be 15 minus, you see it's going to be n minus one right here, right when n is four, n minus one is three. It's going to be, and I'll do it in pink, the 100th term in our sequence, I'll continue our table down, is gonna be what? So 99 times six, actually you could do this in your head. So this right here is 594, and then to figure out what 15, so we wanna figure out, we wanna figure out what 15 minus 594 is, and this can sometimes be confusing, but the way I always process this in my head is I say that this is the exact same thing as the negative of 594 minus 15. So that right there is 579, and then we have this negative sign sitting out there.

Show that the sequence 7, 11, 15, 19, 23, .........

This online tool can help you to find \$n^\$ term and the sum of the first \$n\$ terms of an arithmetic progression.We have the formula that gives the sum of the first n terms of an arithmetic sequence knowing the first and last term of the sequence and the number of terms (see formula above).The term ∑ n is the sum of the first 10 positive integers. You could write out the sequence longhand, but there's a much easier way. For example, write a rule for the sequence 7, 12, 17, 22, 27, . The nth term is given by the arithmetic sequence formula, so all you have to do is plug in the numbers and simplify: Chris Deziel holds a Bachelor's degree in physics and a Master's degree in Humanities, He has taught science, math and English at the university level, both in his native Canada and in Japan. It's easy to figure out an arithmetic sequence when it's only a few terms long, but what if it has thousands of terms, and you want to find one in the middle? The common difference (d) is 5 and the first term (a) is 7.Formulas: The formula for finding \$n^\$ term of an arithmetic progression is \$\color\$, where \$\color\$ is the first term and \$\color\$ is the common difference.The formulas for the sum of first \$n\$ numbers are \$\color\$ and \$\color\$.In other words, we just add the same value each time ... A mathematical sequence is any set of numbers that are arranged in order. An arithmetic sequence is a sequence of numbers in which each term is given by adding a fixed value to the previous term. is an arithmetic sequence because each term is three more than the previous term.In this case, 3 is called the common difference of the sequence.
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