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Question

Which term of the AP 21, 18, 15,...is −81?
(a) 25th
(b) 18th
(c) 35th
(d) 46th

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Solution

(c) 35th
In the given AP, we have
a = 21 and d = (18 - 21) = -3
Let the nth term be -81.
Then a
n = -81
-81 = a + (n - 1)d
-81= 21 + (n - 1) ⨯ (-3)

⇒ -81 = 21 - 3n + 3

-81 = 24 - 3n

⇒ -81 - 24 = -3n

⇒ -105 = -3n
3n = 105
n = 35
Hence, the 35th terms is -81.


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