Question

Find the 30th term of the following sequence. 2,8,14,20

Answer 1

`\large\boxed{a_(30)=176}`

Explanation:

`a_1=2\\a_2=2+6=8\\a_3=8+6=14\\a_4=14+6=20\\\vdots\\\text{It's the arithmetic sequence with common difference d = 6}.\\\\\text{The formula of a n-th term:}\\\\a_n=a_1+(n-1)d\\\\\text{Substitute:}\\\\a_n=2+(n-1)(6)=2+(n)(6)+(-1)(6)=2+6n-6=6n-4\\\\\text{Calculate 30-th term. Substitute}\ n=30:\\\\a_(30)=6(30)-4=180-4=176`