In an arithmetic progression, the third term is 9, and the difference is 20. Find the thirtieth term of this progression.

Let’s use the formula of arithmetic progression to find any of its members:

an = a1 + d * (n – 1),

an – the n-th member,

a1 – 1st term,

d – difference,

n is a sequential number.

a3 = a1 + d * (3 – 1),

a1 = a3 – 2d,

a1 = 9 – 2 * 20 = 9 – 40 = -31.

a30 = a1 + d * (30 – 1),

a30 = -31 + 20 * 29 = -31 + 580 = 549.

Answer: a30 = 549.