Answer to Question #170967 in Algebra for Kim Galvez

Question

. Find the nth term of the following sequences:

a.) 5, 10, 15, 20, …

b.) 22, 18, 14, 10, …

Answer 1

a) We have an arithmetic progression

$$a_1=5, d=10-5=15-10=20-15=5$$

$$a_n=a_1 +d(n-1)$$

$$a_n=5+5(n-1), n=1, 2, ...$$

$$a_n=5n, n=1, 2, ...$$

b) We have an arithmetic progression

$$a_1=22, d=18-22=14-18=10-14=-4$$

$$a_n=a_1 +d(n-1)$$

$$a_n=22+(-4)(n-1), n=1, 2, ...$$

$$a_n=26-4n, n=1, 2, ...$$