Using the formula tn = a + (n -1) × d, find the nth term of the following arithmetic progressions. Class 9

Using the formula tn = a + (n -1) × d, find the nth term of the following arithmetic progressions. Class 9

Question 1.

Using the formula t_n = a + (n -1) × d, find the n^th term of the following arithmetic progressions. Class 9

i. $\frac{1}{2}, \frac{5}{2}, \frac{9}{2}, \frac{13}{2}$

ii. 1.5, 3.5, 5.5, 7.5,...

Answer:

i. Given AP is $\frac{1}{2}, \frac{5}{2}, \frac{9}{2}, \frac{13}{2}$.

Here, a = $\frac{1}{2}$ and d = $\frac{5}{2}-\frac{1}{2}=\frac{4}{2}=2$

∴ t_n = a + (n - 1)d

∴ t_n = $\frac{1}{2}$ + (n - 1) × 2

∴ t_n = $\frac{1}{2}$ + 2n - 2

∴ t_n = 2n - $\frac{3}{2}$

∴ t_n = $\frac{4 n-3}{2}$

ii. Given AP is 1.5, 3.5, 5.5, 7.5

Here, a = 1.5 and d = 3.5 - 1.5 = 2

∴ t_n = a + (n - 1)d

∴ t_n = 1.5 + (n - 1) × 2

∴ t_n = 1.5 + 2n - 2

∴ t_n = 2n - 0.5