The third term in an arithmetic sequence is 10 and the fifth term is 26. If the first term is a1, which is an equation for the nth term of this sequence?

Question

21171 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2017-10-17T13:33:19

#a_n=8n-14#

for an AP

where

#a_1=#the first term

#d=#the common difference
then we have

#a_1, (a_1+d), (a_1+2d),...,a_1+((n-1)d),..#

we are given the third term

#10=a_1+2d--(1)#

and the fifth term

#26=a_1+4d--(2)#

subtract

#(2)-(1)#

#16=2d=>d=8#

sub into#(1)#

#10=a_1+2xx8#

#=>a_1=-6#

so the nth term

#a_n=a+(n-1)#

will be

#a_n=-6+8(n-1)#

#a_n=8n-14#