Verify that the following sequences are arithmetic progressions and write their terms. What do you observe when you plot the ordered pairs emerging from them? (i) 2, 5, 8, 11, … (ii) −5, −1, 3, 7, …
The sequence 2, 5, 8, 11, … is an arithmetic progression with a common difference of 3. Its nth term is t_n = 3n - 1.
The sequence −5, −1, 3, 7, … is an arithmetic progression with a common difference of 4. Its nth term is t_n = 4n - 9.
Explanation
To verify if a sequence is an arithmetic progression (AP), we check if the difference between consecutive terms is constant. For (i), the common difference d = 3, and for (ii), d = 4. Using the nth term formula from the textbook, t_n = a + (n - 1) × d, we calculate the respective nth terms. The textbook also states that plotting ordered pairs from an AP results in points lying on a straight line.