<p>The question is. The first term of a sequence is -3 and every term after the first is 5 more than the term immediately preceding it. What is the value of the 101st term. I know that there is no way I could write out all the numbers so how would I solve this problem?</p>
<p>You can use the arithmetic formula nth term=first term +(n-1)difference or you can solve it with simple logic. </p>
<p>Say you want to know the third term. You start with -3 (the first term) then you add 5 for the second term. Then you add another 5 for the third term. It’s -3+5+5. In other words, you add TWO 5’s when you want to know the THIRD term. </p>
<p>Therefore, if you want the 101st term, you add 100 5’s to the first term. -3+500= 497. </p>
<p>Ok thanks!</p>
<p>Here’s another similar way to solve it:</p>
<p>Start by pretending the sequence starts with 5. So the first term is 5, the second is 2(5) = 10, the third is 3(5) = 15, and so on. Therefore the 101st term is 101(5) = 505. </p>
<p>Now just shift backwards 8 units to get 505 - 8 = 497.</p>
<p>Notes: (1) I started the “shifted” sequence with 5 because we’re adding 5 to get from one term to the next.
(2) By starting with 5 we shifted forward 5 - (-3) = 5 + 3 = 8 units. This is why we must shift back 8 units at the end.</p>