How do you write an explicit formula for the general term of the sequence [-4,2,8,14,...]?

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Answer 1 · 2015-07-17T19:20:08

The explicit formula for the sequence is #color(red)(a_n = 6n-10)#.

This looks like an arithmetic sequence, so we start by finding the common difference #d#.

#d = a_n – a_(n-1)#

Your sequence is #[-4,2,8,14,…]#.

For #a_2#, #d = a_2 - a_1 = 2–(-4) = 2+4 = 6#

For #a_3#, #d = a_3 - a_2 = 8-2 = 6#

For #a_4#, #d = a_4 - a_3 = 14-8 = 6#

So #d=6#.

The general formula for an arithmetic sequence is

#a_n = a_1 + (n-1)d#.

So, for your sequence, the general formula is

#a_n = -4 + 6(n-1) = -4 + 6n-6#.

#a_n = 6n-10#