The first three terms of an arithmetic sequence are 2k+3, 5k-2 and 10k-15, how do you show that k =4?

1 Answer
May 17, 2016

Answer:

Use the definition of an arithmetic sequence to set up a system of two equations and two unknowns and solve.

Explanation:

Since the sequence is arithmetic, there is a number #d# (the "common difference") with the property that #5k-2=(2k+3)+d# and #10k-15=(5k-2)+d#. The first equation can be simplified to #3k-d=5# and the second to #5k-d=13#. You can now subtract the first of these last two equations from the second to get #2k=8#, implying that #k=4#.

Alternatively, you could have set #d=3k-5=5k-13# and solved for #k=4# that way instead of subtracting one equation from the other.

It's not necessary to find, but the common difference #d=3k-5=3*4-5=7#. The three terms in the sequence are 11, 18, 25.