Question

if 3,9,6,12are in A.P then t9-t8=?​

Answer 1

Answer:

a = 3 & d = 9-3 = 6

=a + 8d -[ a + 7d]

=a + 8d -a -7d

= + a & -a will get cut

=8d -7d

=1d

=6.

Step-by-step explanation:

Answer 2

Given,

A.P. $\[ = 3,6,9,12\]$

Solution,

Consider the first term of A.P. is a and common difference is d. Then nth term,

$\[ = a + \left( {n - 1} \right)d\]$

First term, $\[a = 3\]$

Common difference,

$\[\begin{array}{l}d = 6 - 3\\ \Rightarrow d = 3\end{array}\]$

Calculate the 9th term.

$\[\begin{array}{l}{t_9} = a + \left( {9 - 1} \right)d\\ \Rightarrow {t_9} = 3 + \left( {9 - 1} \right)3\\ \Rightarrow {t_9} = 3 + 8 \times 3\\ \Rightarrow {t_9} = 27\end{array}\]$

Calculate the 8th term.

$\[\begin{array}{l}{t_8} = a + \left( {8 - 1} \right)d\\ \Rightarrow {t_8} = 3 + \left( {8 - 1} \right)3\\ \Rightarrow {t_8} = 3 + 7 \times 3\\ \Rightarrow {t_8} = 24\end{array}\]$

Calculate the value of $\[{t_9} - {t_8}\]$

$\[\begin{array}{l} = {t_9} - {t_8}\\ = 27 - 24\\ = 3\end{array}\]$

Hence the value is 3.