Question

A walker is already walking 5km per day and decides to increase this amount by 0.1km per day starting on 1st August.

What distance will he be walking on 3rd August?

b. Is this an arithmetic sequence? Explain your reasoning.

c. What is the formula for the nth term?

Answer 1

Answer: The answers are (a) 5.3 km, (b) Yes, (c) $a_n=5+0.1n.$

Step-by-step explanation:  Given that a walker is walking 5 km per day and he decides that he will increase the distance by 0.1 km per day from 1st August.

(a) On 1st August, he will be walking (5+0.1) = 5.1 km.

On 2nd August, he will be walking (5.1+0.1) = 5.2 km.

On 3rd, August, he will be walking (5.2+0.1) = 5.3 km.

(b) Yes, this sequence is an arithmetic sequence with first term, a = 5.1 and common difference, d = 0.1. Because, the distance 0.1 km is being added, not multiplied.

(c) The formula for the n-th term will be

$a_n=a+(n-1)d\\\\\Rightarrow a_n=5.1+(n-1)\times 0.1\\\\\Rightarrow a_n=5.1+0.1n-0.1\\\\\Rightarrow a_n=5+0.1n.$

Thus, the answers are completed.