Find the common difference of an Arithmetic sequence with the first term and 105th term equal to 3.5.

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d=1

d=0

d=0.5

d=-1

answer is B.

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Detailed Solution

Given that an Arithmetic sequence has a first term and 105th term equal to 3.5.
Let the first term, common difference, nth term be a,d,an respectively.
⇒a=3.5,a105=3.5
For an arithmetic sequence with first term a and common difference d, the nth term is given by,
⇒an=a+(n−1)d
Using this and substituting for nn we get,
⇒a105=a+(105−1)d
Substituting for a,a105 we have,
⇒3.5=3.5+(105−1)d
Subtracting 3.5 from both sides we get,
⇒3.5−3.5=3.5+(105−1)d−3.5
⇒0=104d
The product of two numbers equals zero means either number is zero.
Here, 104≠0 ⇒ d=0
Since d represent the common difference,
we have the common difference of the given sequence is 0.

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