Question

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

Answer 1

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`