Without calculating, determine the following...

Question

You are given two sequences t_n = 4 + (n –1)7 and p_n = 4(2)^n –1. Without calculating, which term is bigger t₅₃₄ or p₅₃₄? Why?

Please answer in an organized and neat/easy to read format. And please only include the information that would be understood by a Grade 11. Thank you :)

Answer 1

check at n=1, t=p

look at function f(n)=4(2)^n –1-4 - (n –1)7

at n=1 f=0

n=2 f=-3

n=3 f=0

n=4 f=7,,,yay it is positive

As n increases f becomes larger, meaning p_n is larger than t_n by an increasing amount

there is no stop to this increase, so at n=534 p_n is larger than t_n