How do you find the 15th term in the arithmetic sequence -3, 4, 11, 18...?

1 Answer
Oct 21, 2016

Answer:

#95#

Explanation:

To find the #n^(th)# term, we use the formula #color (red) (x_n=a+d(n-1))#, where #n# is the term you are looking for, #a# is the #1^(st)# term and #d# is the difference between terms (it does not vary)

From the arithmetic sequence #-3,4,11,18...#, we can see that #a=-3# and #d=7#

You can find #d# by subtracting a number by its precedent #=>d=4-(-3)=7# or #d=11-4=7# and so on! It's always going to be the same value.

So, #x_(15)=-3+7(15-1)=-3+7(14)=-3+98=95#

Another way to do this since it's "only" the #15^(th)# term is by hands or calculator. They already gave you the four terms, which will help you find the difference "#d#". Use only the first term "#-3#" and add 7 until you reach the #15^(th)# term.

#=>-3+7+7+7+7+7+7+7+7+7+7+7+7+7+7=95#

Hope this helps :)