Question

Find the value of APs - 1/15 , 1/12 , 1/10..........to 11th term

Class - X

Solve fast I will give you brainleast marks

Answer 1

Answer:

• a = 1/15
• d = (1/12)-(1/15) = 1/60

Formula:- An = a + (n - 1)d

• 11th term:

➜A11 = 1/15 + (11 - 1)1/60

➜A11 = 1/15 + (10)1/60

➜A11 = 1/15 + 1/6

➜A11 = 21/90

➜A11 = 7/30

• 10th term:

➜A10 = 1/15 + (10 - 1)1/60

➜A10 = 1/15 + (9)1/60

➜A10 = 1/15 + 3/20

➜A10 = 65/300

➜A10 = 13/60

• 9th term:

➜A9 = 1/15 + (9 - 1)1/60

➜A9 = 1/15 + (8)1/60

➜A9 = 1/15 + 2/15

➜A9 = 3/15

• 8th term:

➜A8 = 1/15 + (8 - 1)1/60

➜A8 = 1/15 + (7)1/60

➜A8 = 1/15 + 7/60

➜A8 = 165/900

➜A8 = 11/60

• 7th term:

➜A7 = 1/15 + (7 - 1)1/60

➜A7 = 1/15 + (6)1/60

➜A7 = 1/15 + 1/10

➜A7 = 25/150

➜A7 = 1/6

• 6th term:

➜A6 = 1/15 + (6 - 1)1/60

➜A6 = 1/15 + (5)1/60

➜A6 = 1/15 + 1/12

➜A6 = 27/180

➜A6 = 3/20

• 5th term:

➜A5 = 1/15 + (5 - 1)1/60

➜A5 = 1/15 + (4)1/60

➜A5 = 1/15 + 1/15

➜A5 = 2/15

• 4th term:

➜A4 = 1/15 + (4 - 1)1/60

➜A4 = 1/15 + (3)1/60

➜A4 = 1/15 + 1/20

➜A4 = 35/300

➜A4 = 7/60

$\rule{200}2$

Answer 2

SoluTion:-

☯Given :-

• First term(a_1) = 1/15
• Second term (a_2) = 1/12
• Third term (a_3) = 1/10

☯To find :-

• AP's till 11th term = ?

We know,

$\star\:\large{\boxed{\sf\blue{n^{th} \: term = a + (n - 1)d }}}$

Here,

➩ Common difference (d) = 1/12 - (1/15)

➩ Common difference = 1/12 - 1/15

➩ Common difference = 5 - 4/60

➩ Common difference (d) = 1/60

Now,

➩ $\sf a_4 = \dfrac{1}{15} + (4 - 1)\times \dfrac{1}{60}$

➩ $\sf a_4 = \dfrac{1}{15} + \dfrac{1}{20}$

➩ $\sf a_4 = \dfrac{4 + 3}{60}$

➩ $\green{\boxed{\sf{ a_4 = \dfrac{7}{60} }}}$

•°• 4th term = 7/60

$\rule{200}{1}$

Now,

5th term:-

➩ $\sf a_5 = \dfrac{1}{15} + (5 - 1)\times \dfrac{1}{60}$

➩ $\sf a_5 = \dfrac{1}{15} + \dfrac{1}{15}$

➩ $\sf a_5 = \dfrac{1 + 1}{15}$

➩ $\red{\boxed{\sf {a_5 = \dfrac{2}{15} }}}$

•°• 5th term = 2/15

$\rule{200}{1}$

6th term:-

➩ $\sf a_6 = \dfrac{1}{15} + (6 - 1)\times \dfrac{1}{60}$

➩ $\sf a_6 = \dfrac{1}{15} + \dfrac{1}{12}$

➩ $\sf a_6 = \dfrac{4 + 5}{60}$

➩ $\sf a_6 = \dfrac{9}{60}$

➩ $\blue{\boxed{\sf{ a_6 = \dfrac{3}{20} }}}$

•°• 6th term = 3/20

$\rule{200}{1}$

7th term:-

➩ $\sf a_7 = \dfrac{1}{15} + (7 - 1)\times \dfrac{1}{60}$

➩ $\sf a_7 = \dfrac{1}{15} + \dfrac{1}{10}$

➩ $\sf a_7 = \dfrac{2 + 3}{30}$

➩ $\sf a_7 = \dfrac{5}{30}$

➩ $\green{\boxed{\sf {a_7 = \dfrac{1}{6} }}}$

•°• 7th term = 1/6

$\rule{200}{1}$

8th term:-

➩ $\sf a_8 = \dfrac{1}{15} + (8 - 1)\times \dfrac{1}{60}$

➩ $\sf a_8 = \dfrac{1}{15} + \dfrac{7}{60}$

➩ $\sf a_8 = \dfrac{4 + 7}{60}$

➩ $\red{\boxed{\sf{ a_8 = \dfrac{11}{60} }}}$

•°• 8th term = 11/60

$\rule{200}{1}$

9th term:-

➩ $\sf a_9 = \dfrac{1}{15} + (9 - 1)\times \dfrac{1}{60}$

➩ $\sf a_9 = \dfrac{1}{15} + \dfrac{2}{15}$

➩ $\sf a_9 = \dfrac{1 + 2}{15}$

➩ $\sf a_9 = \dfrac{3}{15}$

➩ $\blue{\boxed{\sf{a_9 = \dfrac{1}{5} }}}$

•°• 9th term = 1/5

$\rule{200}{1}$

10th term:-

➩ $\sf a_{10} = \dfrac{1}{15} + (10 - 1)\times \dfrac{1}{60}$

➩ $\sf a_{10} = \dfrac{1}{15} + \dfrac{3}{20}$

➩ $\sf a_{10} = \dfrac{4 + 9}{60}$

➩ $\green{\boxed{\sf{a_{10} = \dfrac{13}{60} }}}$

•°• 10th term = 13/60

$\rule{200}{1}$

Let me show you the 11th term.

11th term:-

➩ $\sf a_{11} = \dfrac{1}{15} + (11 - 1)\times \dfrac{1}{60}$

➩ $\sf a_{11} = \dfrac{1}{15} + \dfrac{1}{6}$

➩ $\sf a_{11} = \dfrac{2 + 5}{30}$

➩ $\red{\boxed{\sf{a_{11} = \dfrac{7}{30} }}}$

•°• 11th term = 7/30