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 #1 : 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 #5 : 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 #2 : Nth Term Of An Arithmetic Sequence
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 #22 : Sequences
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 .
Example Question #2 : How To Find The Nth Term Of An Arithmetic Sequence
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 formula for the series; = –30