How do you find the first term and common difference if The 6th term of the sequence is -2, The 14th term of the sequence is -18?

1 Answer
Jun 10, 2016

Answer:

First term: #8#
Common difference: #(-2)#

Explanation:

For an arithmetic sequence, #a_i#, with a common difference of #d#
#color(white)("XXX")color(red)(a_(k+n)=a_k+n*d)#

We are told
#color(white)("XXX")a_14=-18color(white)("XX")andcolor(white)("XX")a_6=-2#

Using #k=6# we have #n=8#
#color(white)("XXX")a_14=color(red)(a_(6+8)=a_6+8*d)#

#color(white)("XXX")-18=-2+8d#

#color(white)("XXX")rarr d=-2#

Now setting #k=1#
#color(white)("XXX")a_6=color(red)(a_(1+5)=a_1+5xx(-2))#

#color(white)("XXX")rarr -2 = a_1+(-10)#

#color(white)("XXX")rarr a_1=8#