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Question
Two APs have the same common difference. The first term of one of these is 3, and that of the other is 8. What is the difference between their 2nd terms ?
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Solution
Let the common difference of the two APs be d.
Then, their nth terms are
an=3+(n−1)d and bn=8+(n−1)d
an−bn=[3+(n−1)d]−[8+(n−1)d]
an−bn=3+(n−1)d−8−(n−1)d
an−bn=3−8
an−bn=−5 for all n∈N
Therefore,a2−b2=−5
Then, their nth terms are
an=3+(n−1)d and bn=8+(n−1)d
an−bn=[3+(n−1)d]−[8+(n−1)d]
an−bn=3+(n−1)d−8−(n−1)d
an−bn=3−8
an−bn=−5 for all n∈N
Therefore,
a2−b2=−5
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