How do you write the first five terms of the arithmetic sequence given #a_8=26, a_12=42#?

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Answer 1 · 2018-08-08T06:27:37

#-2, 2, 6, 10, 14#

The general term of an arithmetic sequence is given by the formula:

#a_n = a + d(n-1)#

where #a# is the initial term and #d# the common difference.

Given #a_8 = 26# and #a_12 = 42#, we find:

#16 = 42-26#

#color(white)(16) = a_12 - a_8#

#color(white)(16) = (a+11d) - (a+7d)#

#color(white)(16) = 4d#

Hence #d=4#

Then:

#26 = a_8 = a+7d = a+28#

Hence #a=-2#

So the first five terms of the sequence are:

#-2, 2, 6, 10, 14#