Question Type 1: Finding the nth term given the first term and the common difference Exercises

On a bus route, the first stop is $2 \text{ km}$ from the depot, and each following stop is $0.85 \text{ km}$ further than the previous one. How far from the depot is the 30th stop?

Find the 10th term of the arithmetic sequence with first term $u_1 = -2$ and common difference $d = 4$.

Find the 15th term of the arithmetic sequence with first term $u_1 = 7$ and common difference $d = 5$.

Find the 6th term of the arithmetic sequence with first term $u_1 = 3$ and common difference $d = 8$.

Find the 5th term of the arithmetic sequence with first term $u_1 = 20$ and common difference $d = -5$.

Find the 12th term of the arithmetic sequence with first term $u_1 = 1.5$ and common difference $d = 0.75$.

Each step of a staircase increases in height by $2 \text{ cm}$. If the first step is $15 \text{ cm}$ high, what is the height of the 10th step?

Find the 25th term of the arithmetic sequence with first term $u_1 = 0$ and common difference $d = 7$.

Find the 8th term of the arithmetic sequence with first term $u_1 = 12$ and common difference $d = -3$.

A student reads 10 pages on the first day and increases the number of pages by 5 each subsequent day. How many pages will they read on the 20th day?

A savings plan starts with $u_1 = \text{£}50$ in the first month and you add £20 each month. What is the amount in the 18th month?

Find the 12th term of the arithmetic sequence with first term $u_1 = 100$ and common difference $d = -10$.