Mathematics
The 7th term of an A.P. is −1 and its 16th term is 17. The nth term of the A.P. is :
(3n + 12)
(2n − 5)
(3n + 5)
(2n − 15)
AP
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Answer
We know that,
an = a + (n - 1)d
The 7th term of an A.P. is −1.
a + 6d = -1 ……(1)
The 16th term of an A.P. is 17.
a + 15d = 17 ……(2)
Subtract Equation (1) from Equation (2) :
⇒ a + 15d - (a + 6d) = 17 - (-1)
⇒ a + 15d - a - 6d = 18
⇒ 9d = 18
⇒ d =
⇒ d = 2.
Substituting d = 2 into Equation (1), we get :
⇒ a + 6(2) = -1
⇒ a + 12 = -1
⇒ a = -1 - 12
⇒ a = -13.
Now,
⇒ an = a + (n - 1)d
⇒ an = -13 + (n - 1)2
= -13 + 2n - 2
= 2n - 15.
Hence, option 4 is the correct option.
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