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.
An 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 Comments are closed.

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