Question

Prove that the sequence defined by an=4n+5 is an arithmetic progression and find common difference

Answer 1

Answer:

an = 4n + 5

a1 = 4+5 = 9

a2 = 4(2) + 5 = 8 + 5 = 13

a3 = 4(3) + 5 = 12 + 5 = 17

if a2 - a1 = a3 -a2, the given sequence is an ap.

a2 - a1 = 13 -9 =4.

a3 - a2 = 17 -13 = 4.

therefore, a3 - a2 = a2 - a1 = d = 4,

therefore, the sequence defined by an=4n+5 is an ap

Step-by-step explanation:

Answer 2

An=4n+5  

n(1)=4₁+5=9  

n(2)=4²+5=13  

n(3)=4³+5=17  

therefore difference =17-13=4