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

## Example Questions

### Example Question #1 : Arithmetic Sequences

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

Saturday

Tuesday

Wednesday

Monday

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 #1 : Arithmetic Sequences

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 #1 : Nth Term Of An Arithmetic Sequence

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 #4 : Arithmetic Sequences

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 #1 : Arithmetic Sequences

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 #1 : 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