Answer: The answers are (a) 5.3 km, (b) Yes, (c) ![a_n=5+0.1n.](https://tex.z-dn.net/?f=a_n%3D5%2B0.1n.)
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.](https://tex.z-dn.net/?f=a_n%3Da%2B%28n-1%29d%5C%5C%5C%5C%5CRightarrow%20a_n%3D5.1%2B%28n-1%29%5Ctimes%200.1%5C%5C%5C%5C%5CRightarrow%20a_n%3D5.1%2B0.1n-0.1%5C%5C%5C%5C%5CRightarrow%20a_n%3D5%2B0.1n.)
Thus, the answers are completed.