Find the second term and nth term of an AP whose 6th term is 12 and 8th term is 22.
A
a2=−9,an=3n−43
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B
a2=7,an=3n−52
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C
a2=−8,an=5n−18
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D
a2=−9,an=5n−38
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Solution
The correct option is Ca2=−8,an=5n−18 Let a and d be the first term and the common difference of the given AP respectively. Then, a6=12⇒a+5d=12 ...(1) a8=22⇒a+7d=22 ...(2) On subtracting (2) from (1), we get 2d=10⇒d=5 Putting d=5 in (1), we get a=12−5×5=−13 Now, a2=a+d=−13+5=−8 and an=a+(n−1)d