# How do you determine whether the sequence #ln1, ln2, ln3, ln4, ln5,...# is arithmetic and if it is, what is the common difference?

##### 1 Answer

Aug 22, 2017

the terms are **not** part of an AP

#### Explanation:

The term of an AP sequence takes the form:

# { a, a+d, a+2d, a+3d, , ... } #

Where:

#a = # first term

#d = # common difference

If the given sequence:

# { ln1, ln2, ln3, ... } #

were an AP the clearly we have first term given by:

#a= ln1 \ \ \ (=0)#

And the second term would satisfy:

# a+d=ln2 #

# => ln1+d=ln2 #

# => d = ln2-ln1 = ln2 #

Thus, the third term would be given by:

# a+2d = ln1+2*ln2 =ln 4 != ln3#

Hence, the terms are **not** part of an AP