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Question

Find the second term and nth term of an AP whose 6th term is 12 and 8th term is 22.

A
a2 =9, an =3n43
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B
a2 =7, an =3n52
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C
a2 =8, an =5n18
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D
a2 =9, an =5n38
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Solution

The correct option is C a2 =8, an =5n18
Let a and d be the first term and the common difference of the given AP respectively. Then,
a6=12a+5d=12 ...(1)
a8=22a+7d=22 ...(2)
On subtracting (2) from (1), we get
2d=10d=5
Putting d=5 in (1), we get
a=125×5=13
Now, a2=a+d=13+5=8 and
an=a+(n1)d
=13+(n1)×5
=5n18

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