Mathematics
The 6th term of an A.P. is 16 and the 14th term is 32. Determine the 36th term.
AP
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Answer
Let the first term be a and common difference be d of the A.P.
Given,
⇒ a6 = a + (6 - 1)d
⇒ a + 5d = 16 ……..(i)
⇒ a14 = a + (14 - 1)d
⇒ a + 13d = 32 ……..(ii)
Subtracting (i) from (ii) we get,
⇒ a + 13d - (a + 5d) = 32 - 16
⇒ 8d = 16
⇒ d = 2.
Substituting value of d in (i) we get,
⇒ a + 5(2) = 16
⇒ a + 10 = 16
⇒ a = 6.
a36 = a + (36 - 1)d = 6 + (35)(2) = 76.
Hence, 36th term = 76.
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