Question

find the common difference of AP log2,log 4, log8,............​

Answer 1

Answer:

The common difference is log 2

Answer 2

The common difference (d) of the given AP = $\log2$

Step-by-step explanation:

The given AP are:

$\log2, \log 4, \log8,..........$

To find, the common difference (d) of the given AP = ?

∴ $\log2, \log 4, \log8,..........$

= $\log2, \log 2^2, \log 2^3,..........$

= $\log2, 2\log 2, 3\log 2,..........$ [ ∵ $\log a^{m}=m\log a$]

Here, first term ($a_{1}$) = $\log2$, second term($a_{2}$) = $2\log 2$ and third term$(a_{3})$ = $3\log 2$

We know that,

The common difference (d) = Second term($a_{2}$) - First term ($a_{1}$)

=Third term$(a_{3})$ - Second term($a_{2}$)

∴ Second term($a_{2}$) - First term ($a_{1}$) = $2\log 2$ - $\log2$ = $\log2$

Also,

Third term$(a_{3})$ - Second term ($a_{2}$)  = $3\log 2$ - $2\log 2$ = $\log2$

∴ The common difference (d) of the given AP = $\log2$