find the second term and nth term of an ap whose 6th term is 12 and the 8th term is 22
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Given, a₆=a+5d=12--------(1)
And a₈=a+7d=22----------(2)
Eq(2)-Eq(1)⇒2d=10
⇒d=10/2
⇒d=5
Substituting d=5 in(1),
a+5(5)=12
⇒a=12-25
⇒a=-13
Therefore, the second term of the AP,a₂=a+d=(-13)+5=-8
And nth term of the AP=a+(n-1)d
=(-13)+(n-1)5
=(-13)+5n-5
=5n-18
And a₈=a+7d=22----------(2)
Eq(2)-Eq(1)⇒2d=10
⇒d=10/2
⇒d=5
Substituting d=5 in(1),
a+5(5)=12
⇒a=12-25
⇒a=-13
Therefore, the second term of the AP,a₂=a+d=(-13)+5=-8
And nth term of the AP=a+(n-1)d
=(-13)+(n-1)5
=(-13)+5n-5
=5n-18
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