All ACT Math Resources
Example Question #1 : How To Find The Nth Term Of An Arithmetic Sequence
If the first day of the year is a Monday, what is the 295th day?
The 295th day would be the day after the 42nd week has completed. 294 days/7 days a week = 42 weeks. The next day would therefore be a monday.
Example Question #2 : How To Find The Nth Term Of An Arithmetic Sequence
If the first two terms of a sequence are and , what is the 38th term?
The sequence is multiplied by each time.
Example Question #2 : Arithmetic Sequences
Find the sum of the first fifteen terms in an arithmetic sequence whose sixth term is and whose ninth term is .
Use the formula an = a1 + (n – 1)d
a6 = a1 + 5d
a9 = a1 + 8d
Subtracting these equations yields
a6 – a9 = –3d
–7 – 8 = –3d
d = 5
a1 = 33
Then use the forumula for the series; = –30
Example Question #3 : Arithmetic Sequences
Find the term of the following sequence:
The formula for finding the term of an arithmetic sequence is as follows:
= the difference between consecutive terms
= the number of terms
Therefore, to find the term:
Example Question #4 : Arithmetic Sequences
What is the rd term of the following sequence:?
Notice that between each of these numbers, there is a difference of ; however the first number is , the second , and so forth. This means that for each element, you know that the value must be , where is that number's place in the sequence. Thus, for the rd element, you know that the value will be or .
Example Question #1 : Nth Term Of An Arithmetic Sequence
What is the th term in the following series of numbers: ?
Notice that between each of these numbers, there is a difference of . This means that for each element, you will add . The first element is or . The second is or , and so forth... Therefore, for the th element, the value will be or .