Question

The first three terms of an arithmetic sequence are u1=3k−1, u2=4k+1, and u3=6k−2. What is the value of k?

Answer 1

• From common difference of an arithmetic progression:

`{ \tt{u _(3) - u _(2) = u _(2) - u _(1) }}`

• substitute into the expression above:

`{ \tt{ \{(6k - 2) - (4k + 1) \}} = \{(4k + 1) - (3k - 1) \}} \\ \\ { \tt{6k - 4k - 2 - 1 = 4k - 3k + 1 + 1}} \\ \\ { \tt{2k - 3 = k + 2}} \\ \\ { \tt{2k - k = 2 + 3}} \\ \\ { \underline{ \underline{ \bf{ \: \: k = 5 \: \: }}}}`