Determine whether the sequence ln1,ln2,ln3,ln4,ln5,... is arithmetic and if it is, what is the common difference

beninar6u

beninar6u

Answered question

2022-10-09

Determine whether the sequence ln1,ln2,ln3,ln4,ln5,... is arithmetic and if it is, what is the common difference

Answer & Explanation

Derick Ortiz

Derick Ortiz

Beginner2022-10-10Added 11 answers

The term of an AP sequence takes the form:
{ a , a + d , a + 2 d , a + 3 d , , ... }
Where:
a=first term
d=common difference
If the given sequence:
{ ln 1 , ln 2 , ln 3 , ... }
were an AP the clearly we have first term given by:
a = ln 1       ( = 0 )
And the second term would satisfy:
a + d = ln 2
ln 1 + d = ln 2
d = ln 2 - ln 1 = ln 2
Thus, the third term would be given by:
a + 2 d = ln 1 + 2 ln 2 = ln 4 ln 3
Hence, the terms are not part of an AP

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