How do you write the nth term rule for the arithmetic sequence with #a_5=17# and #a_15=77#?

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Answer 1 · 2016-07-28T10:37:23

#a_n=6n-13, n in NN#.

Let #a_1, a_n and d!=0# denote the first , #n^(th)# and common difference for the Arithmetic Sequence in question.

Then, we know that, #a_n=a_1+(n-1)d...........(1)#

Given that #a_5=17#, so, taking #n=5# in #(1)#, we have,

#a_1+4d=17...............(2)#.

Similarly, #a_15=77 rArr a_1+14d=77.................(3)#

Solving #(2) & (3), d=6, and, a_1=-7#.

These, with #(1)# gives #a_n=6n-13, n in NN#.