How do you write a rule for the nth term of the arithmetic sequence given #a_6=13, a_14=25#?

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Answer 1 · 2018-04-19T15:38:07

#color(blue)(4+3/2n)#

The nth term of an arithmetic sequence is given as:

#a+(n-1)d#

Where #bba# is the first term, #bbd# is the common difference and #bbn# is the nth term.

We need to find the first term and the common difference:

#a_6=13=>a+(6-1)d=13#

#a_14=25=>a+(14-1)d=25#

#a+5d=13 \ \ \ \[1]#

#a+13d=25 \ \ \ \ \[2]#

Solving simultaneously:

Subtract #[1]# form #[2]#

#0+8d=12=>d=3/2#

Substituting this in #[1]#

#a+5(3/2)=13#

#a=13-3(3/2)=11/2#

For nth term:

#11/2+(n-1)(3/2)=11/2+3/2n-3/2=color(blue)(4+3/2n)#