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In order for us to know how to obtain terms that are far down these lists of numbers, we need to develop a formula that can be used to calculate these terms. If we were to try and find the 20th term, or worse to 2000th term, it would take a long time if we were to simply add a number  one at a time  to find our terms.
I am stressed over the th for ex An= (2n + 1)
________
2
If a 5yearold was asked what the 301st number is in the set of counting numbers, we would have to wait for the answer while the 5yearold counted it out using unnecessary detail. We already know the number is 301 because the set is extremely simple; so, predicting terms is easy. Upon examining arithmetic sequences in greater detail, we will find a formula for each sequence to find terms
I have looked at the fixed number, called the common difference (d), is 3; so, the formula will be an = dn + c or an = 3n + c, where c is some number that must be found.
For sequence A above, the rule an = 3n + c would give the values...
31 + c = 3 + c
32 + c = 6 + c
33 + c = 9 + c
34 + c = 12 + c
35 + c = 15 + c
If we compare these values with the ones in the actual sequence, it should be clear that the value of c is 2. Therefore the formula for the nth term is...
an = 3n + 2.
Now if we were asked to find the 37th term in this sequence, we would calculate for a37 or 3(37) + 2 which is equal to 111 + 2 = 113. So, a37 = 113, or the 37th term is 113. Likewise, the 435th term would be a435 = 3(435) + 2 = 1307.
I am stressed over the th for ex An= (2n + 1)
________
2
If a 5yearold was asked what the 301st number is in the set of counting numbers, we would have to wait for the answer while the 5yearold counted it out using unnecessary detail. We already know the number is 301 because the set is extremely simple; so, predicting terms is easy. Upon examining arithmetic sequences in greater detail, we will find a formula for each sequence to find terms
I have looked at the fixed number, called the common difference (d), is 3; so, the formula will be an = dn + c or an = 3n + c, where c is some number that must be found.
For sequence A above, the rule an = 3n + c would give the values...
31 + c = 3 + c
32 + c = 6 + c
33 + c = 9 + c
34 + c = 12 + c
35 + c = 15 + c
If we compare these values with the ones in the actual sequence, it should be clear that the value of c is 2. Therefore the formula for the nth term is...
an = 3n + 2.
Now if we were asked to find the 37th term in this sequence, we would calculate for a37 or 3(37) + 2 which is equal to 111 + 2 = 113. So, a37 = 113, or the 37th term is 113. Likewise, the 435th term would be a435 = 3(435) + 2 = 1307.
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An= (2n + 1)
________
2
I get the n is the format for the ans.