How do I find the #n#th term of an arithmetic sequence?

1 Answer
Alan P.
Mar 25, 2016

#a_n=a_1+(n-1)*d#
#color(white)("XXX")#where #a_1# is the first term and
#color(white)("XXXXXXX")d# is the difference between a term and its previous term.

Explanation:

Examine the pattern:

#a_1#
#a_color(brown)(2)=a_1+d=color(green)(a_1+1d)#
#a_color(brown)(3)=a_2+d=a_1+d+d=color(green)(a_1+2d)#
#a_color(brown)(4)=a_3+d=a_1+2d+dcolor(green)(=a_1+3d)#
#a_color(brown)(5)=a_4+d=a_1+3d+d=color(green)(a_1+4d)#

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