How do you find an equation that describes the sequence #7, 10, 13, 16,...# and find the 89th term?

2 Answers
Oct 27, 2017

Answer:

Arithmatic sequene with common diference #3# and
#89# th term is #271#

Explanation:

This is an arithmatic sequene , the common difference is

#d=16-13=13-10=10-7=3 ; 1#st term is #a=7#

#n# th term is #t_n=a+(n-1)d :. 89# th term is

#t_89=7+(89-1)3= 7+264=271#

#89# th term is #271# [Ans]

Oct 27, 2017

Answer:

#a_n=3n+4,a_(89)=271#

Explanation:

#"the given terms are the terms of an "color(blue)"arithmetic sequence"#

#a,a+d,a+2d,a+3d,...... ,a+(n-1)d#

#"where a is the first term and d the "color(blue)"common difference"#

#d=a_2-a_1=a_3-a_2=......=a_n-a_(n-1)#

#"here "d= 10-7=13-10=16-13=3#

#"the nth term of the sequence is"#

#•color(white)(x)a_n=a+(n-1)d#

#rArra_n=7+3(n-1)=7+3n-3#

#rArra_n=3n+4larrcolor(red)"nth term formula for sequence"#

#rArra_(89)=(3xx89)+4=271#