What is the sum of the sequence #6, 12, 18, 24, 30, 36, 42#?

1 Answer
Jun 25, 2016

168

Explanation:

This is an #color(blue)"arithmetic sequence"# recognisable because there is a common difference (d) between the terms

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

here d = 12 - 6 =18 - 12 = 6

To calculate the sum to n terms of the sequence.

#color(red)(|bar(ul(color(white)(a/a)color(black)(S_n=n/2[2a+(n-1)d])color(white)(a/a)|)))#
where a is the 1st term and d the common difference.

here a = 6 , d = 6 and n = 7

#rArrS_7=7/2[(2xx6)+(6xx6)]=7/2(12+36)=168#