An arithmetic sequence has first term a. The 4th term of the sequence is ka. The 7th term of the sequence is 9a. Find the value of k?

1 Answer
Jim G.
Nov 17, 2017

#k=5#

Explanation:

#"the nth term of an "color(blue)"arithmetic sequence "# is.

#•color(white)(x)a_n=a+(n-1)d#

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

#a_4=a+(4-1)d)=a+3d=kato(1)#

#a_7=a+(7-1)d=a+6d =9ato(2)#

#"to eliminate a subtract equation "(1)" from "(2)#

#(a-a)+(6d-3d)=(9a-ka)#

#rArr3d=9a-ka#

#"substitute this value into equation "(1)#

#a+9a-ka=ka#

#rArr10a-ka=ka#

#"add "ka" to both sides"#

#10acancel(-ka)cancel(+ka)=ka+ka#

#rArr2ka=10arArrk=(10a)/(2a)=5#

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