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
