If a1=5 and a5=15, how do you find the formula for the nth term of the sequence?

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Answer 1 · 2015-08-31T07:07:41

# color(blue)(a_n = 5+(n-1) *5/2)#

#a_1 = color(blue)(5#
#a_5=15#

The #nth# term is denoted as:

#a_n = a_1+(n-1)d#

So,
#a_5=a_1+(5-1)*d#

#15=5 +4d#

#15-5=4d#

#10=4d#

#d=10/4#

#color(blue)(d=5/2#

So the formula for #nth# term can now be written as:
#a_n = a_1+(n-1)d#

# color(blue)(a_n = 5+(n-1) *5/2)# where #(n =1,2,3...)#