Question

if the 7th term of an ap is 1/12 and 12th term is 1/7 then it's 168th term is​

Answer 1

Step-by-step explanation:

1/12=a+(7-1)d. ______________[1]

1/7=a+(12-1)d. ______________[2]

from [1] and [2],

1/12 - 1/7 = -5d

5/84 = 5d

d= 1/84 ]-----------------

a = 1/12 - 1/14

a = 1/84 ]---------------

T = a + (168-1)d

= 1/84 + (168-1) 1/84

--------------------[T = 2 ]--------------------------

Answer 2

Answer:

2

Step-by-step explanation:

Given :-

$\bull \: \: \: seventh \: term, a_7= \frac{1}{12}$

$\bull \: \: twelvth \: term,a_{12 }= \frac{1}{7}$

To find :-

$\bull \: \: one-sixty \: eighth \: term, a_{168}$

Now using the given conditions,

$a_7 = a + (7 - 1)d = \frac{1}{12}$

$\implies \: a + 6d = \frac{1}{12} \: \: \: \: \: \: \: \: \: \: \: (1)$

$a_{12} = a + (12 - 1)d = \frac{1}{7}$

$\implies \: a + 11d = \frac{1}{7} \: \: \: \: \: \: \: \: \: \: \: (2)$

Subtracting equation 1 from 2

$\not \: a + 6d = \frac{1}{12} \\ \not a + 11d = \frac{1}{7} \\ \underline{- \: \: \: \: \: - \: \: \: \: \: - } \\ - 5d = \frac{ - 5}{84}$

$- 5d = - \frac{5}{84}$

$\boxed{d = \frac{1}{84} }$

Now put the value of d in equation 1

$a + 6( \frac{1}{84} ) = \frac{1}{12}$

$a + \frac{6}{84} = \frac{1}{12}$

$a = \frac{1}{12} - \frac{6}{84}$

$a = \frac{7 - 6}{84}$

$</u></em></strong><strong><em><u>\</u></em></strong><strong><em><u>b</u></em></strong><strong><em><u>o</u></em></strong><strong><em><u>x</u></em></strong><strong><em><u>e</u></em></strong><strong><em><u>d</u></em></strong><strong><em><u>{</u></em></strong><strong><em><u>a = \frac{1}{84} </u></em></strong><strong><em><u>}</u></em></strong><strong><em><u>$

Now 168th term will be

$a_{168} = \frac{1}{84} + \frac{167}{84}$

$a_{168} = \frac{168}{84}$

$\boxed{a_{168} = 2}$

Hence it's 168 term will be 2