The values of several terms of a sequence are shown in the table.

Find the first term,

*f(1)*.
Check to see if it is an arithmetic sequence by determining if there is a common difference.

12 - 5

———- {subtracted second from fourth and divided by 2}

2

= 7/2 {subtracted 12 - 5}

= 3.5 {divided by 2}

12 + 3.5 + 3.5 + 3.5

= 22.5 {the seventh term}

5 - 3.5 {subtracted the common difference, 3.5, from the second term to arrive at the first}

= 1.5 {subtracted}

**An**

A

Find the difference between the second and fourth numbers and divide by two, to determine the common difference:__arithmetic sequence__is a sequence of numbers such that the__difference__of any two successive numbers of the sequence__is a constant__.A

__geometric sequence__is a sequence of numbers in which the__ratio__between any two successive numbers__is a constant__.Find the difference between the second and fourth numbers and divide by two, to determine the common difference:

12 - 5

———- {subtracted second from fourth and divided by 2}

2

= 7/2 {subtracted 12 - 5}

= 3.5 {divided by 2}

**It appears the common difference may be 3.5.****Keep adding 3.5 to each term to see if you can go from the fourth term and land on the seventh term.**12 + 3.5 + 3.5 + 3.5

= 22.5 {the seventh term}

**The common difference is 3.5.****Find the first term by subtracting 3.5 from the second term, 5.**5 - 3.5 {subtracted the common difference, 3.5, from the second term to arrive at the first}

= 1.5 {subtracted}

**The first term,***f(1)*, is 1.5__Ask Algebra House__