# ACT Math : How to find the nth term of an arithmetic sequence

## Example Questions

### Example Question #1681 : Act Math

If the first day of the year is a Monday, what is the 295th day?

Monday

Wednesday

Tuesday

Saturday

Monday

Explanation:

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?

Explanation:

The sequence is multiplied by each time.

### Example Question #1686 : Act Math

Find the  term of the following sequence:

Explanation:

The formula for finding the  term of an arithmetic sequence is as follows:

where

= the difference between consecutive terms

= the number of terms

Therefore, to find the  term:

### Example Question #1 : How To Find The Nth Term Of An Arithmetic Sequence

What is the rd term of the following sequence:?

Explanation:

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 #4 : Nth Term Of An Arithmetic Sequence

What is the th term in the following series of numbers: ?

148

Explanation:

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 .

Explanation:

Use the formula an = a1 + (n – 1)d

a6 = a1 + 5d

a9 = a1 + 8d

Subtracting these equations yields

a– a9 = –3d

–7 – 8 = –3d

d = 5

a1 = 33

Then use the formula for the series; = –30