Mathematics
If the third term of an A.P. is 5 and the seventh term is 9, find the 17th term.
AP
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Answer
We know that,
nth term of an A.P. is given by,
an = a + (n - 1)d
Given, 3rd term is 5
∴ a3 = a + (3 - 1)d
⇒ 5 = a + 2d
⇒ a + 2d = 5 ……..(i)
Given, 7th term is 9
∴ a7 = a + (7 - 1)d
⇒ 9 = a + 6d
⇒ a + 6d = 9 ……..(ii)
Subtracting (i) from (ii) we get,
⇒ a + 6d - (a + 2d) = 9 - 5
⇒ 4d = 4
⇒ d = 1.
Substituting value of d in (i) we get,
⇒ a + 2(1) = 5
⇒ a + 2 = 5
⇒ a = 3.
17th term = a17
a17 = a + (17 - 1)d
= 3 + 16(1)
= 3 + 16
= 19.
Hence, 17th term of A.P. = 19.
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