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Question
Determine the nth term of the AP whose 7th term is -1 and 16th term is 17.
Solution
Let a be the first term and d be the common difference of the AP. Then,
a7 = -1
⇒ a + (7-1) d = -1 [ an = a + (n-1)d]
⇒ a+ 6d = -1 .................(1)
Also ,
a16 = 17
⇒ a + 15d = 17 .................(2)
from (1)and (2), we get
-1-6d+15d=17
⇒9d = 17 + 1 =18
⇒ d= 2
Putting d = 2 in (1), we get
a+6×2=-1
⇒ a = -1-12=-13
∴ an = a+ (n-1)d
=-13 +(n-1) × 2
=2n -15
Hence, the nth term of the AP is (2n - 15).
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