# ACT Math : nth Term of an Arithmetic Sequence

## Example Questions

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### Example Question #1 : Nth Term Of An Arithmetic Sequence

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 #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 : Arithmetic Sequences

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 #9 : 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 #10 : 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 : 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

### Example Question #1 : How To Find The Next Term In An Arithmetic Sequence

Given the sequence of numbers:

1, 5, 9, _ , _ , 21 ....

What are the two missing terms of the arithmetic sequence?

13, 16

14, 17

13, 17

12, 18

14, 16

13, 17

Explanation:

The sequence is defined by a= 4n – 3  for such n = 1,2,3,4....

### Example Question #2 : How To Find The Next Term In An Arithmetic Sequence

What is the next term in the following sequence?

Explanation:

What is the next term in the following sequence?

This is an arithmetic sequence with a common difference of . To find the next term in an arithmetic sequence, add the common difference to the previously listed term:

### Example Question #3 : How To Find The Next Term In An Arithmetic Sequence

Find the sixth term in the following number sequence.

Explanation:

This question can be answered by analyzing the sequence provided and determining the pattern. The first term is , and the second term is  The third term is Thus,  has been added to  in order to obtain , and  has been added to  in order to obtain  This shows that  is added to each preceding term in the sequence in order to obtain the next term. The complete sequence from terms one through six is shown below.

Thus, the sixth term is

### Example Question #4 : How To Find The Next Term In An Arithmetic Sequence

What is the next term of the series ?

Explanation:

Begin by looking at the transitions from number to number in this series: