What is the 13th term in an arithmetic sequence whose first term is 10 and whose 4th term is 1?

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Answer 1 · 2016-06-22T18:31:12

#-26.#

Let the first term of an A.P. be a , common diff. be d , #d!=0,# & the #n^(th)# term be #t_n.#

Then, we have the formula : #t_n=a+(n-1)d............(1)#

In our case, #a=10, n=4, t_4=1.#Using these values in #(1),#

#1=10+3d,# giving, #d=-3.#

Hence, in #(1)#, #a=10,d=-3,# so, #t_n=10-3(n-1)=10-3n+3=13-3n.#

#:.# Reqd. Term#=t_13=13-39=-26.#