Find recursive rules for the APs in the previous exercises. Class 9

Find recursive rules for the APs in the previous exercises. Class 9

Question 1.

Find recursive rules for the APs in the previous exercises. Class 9

Answer:

i. Consider AP: $\frac{1}{2}, \frac{5}{2}, \frac{9}{2}, \frac{13}{2} \ldots$

Here, first term t₁ = $\frac{1}{2}$

common difference = $\frac{5}{2}-\frac{1}{2}=\frac{4}{2}=2$

Recursive rule is t₁ = $\frac{1}{2}$ and t_n = t_n-1 + 2 for n ≥ 2

ii. Consider AP: 1.5, 3.5, 5.5, 7.5...

Here, first term t₁ = 1.5

Common difference = 3.5 - 1.5 = 2

Recursive rule is t₁ = 1.5 and t_n = t_n-1 + 2 for n ≥ 2

Question 2.

Can the same approach be used to find the sum of 1 + 2 + 3 +...+ 100? Class 9

Answer:

Yes, the same approach can be used to find the sum of 1 + 2 + 3 +...+ 100.

Let S = 1 + 2 + 3 + ... + 100

and S = 100 + 99 + 98 + ... + 1

By adding both, we get

2S = 101 + 101 + 101 +...+ 101 (100 times)

∴ 2S = 10100

∴ S = $\frac{10100}{2}$ = 5050