Question

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

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.