Question

समान्तर श्रेढी
8. एक सूत्र द्वारा ज्ञात कीजिए कि 10 और 100 के बीच में कितने पूर्णांक 3 से विभाजित होंगे ?
How many integers between 10 and 100 are divisible by 3 ? Solve by a formula.​

Answer 1

Step-by-step explanation:

Numbers divisible by 3 between 10 and 100 are given as:

12, 15, 18, 21,...................99

Here

first term a = 12

Common Difference d = 3

$t_n$= 99

n =?

$\because \: t_n = a + (n - 1)d \\ \\ \therefore \: 99 = 12 + (n - 1) \times 3 \\ \\ \therefore \: 99 - 12 = (n - 1) \times 3\\ \\ \therefore \: 87 = (n - 1) \times 3 \\ \\\therefore \frac{87}{3} = n - 1\\ \\\therefore 29 = n - 1 \\ \\\therefore n = 29 + 1 \\ \\ \huge \purple{ \boxed{\therefore n = 30}}$

Hence, there are total 30 integers between 10 and 100 which are are divisible by 3.