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प्रश्न
The 17th term of AP is 5 more than twice its 8th term. If the 11th term of the AP is 43, find its nth term.
उत्तर
Let a be the first term and d be the common difference of the AP. Then,
a17 = 2as +5 (Given)
∴ a + 16d = 2 (a+7d)+5 [an = a +(n-1) d]
⇒ a + 16d = 2a + 14d +5
⇒ a-2d =-5 .............(1)
Also,
a11 = 43 (Given)
⇒ a + 10d = 43 ................(2)
From (1) and (2), we get
-5 +2d + 10d = 43
⇒ 12d = 43+5 = 48
⇒ d=4
Putting d = 4 in (1), we get
a-2 × 4 =-5
⇒ a= -5 + 8=3
∴ an = a +(n-1) d
= 3 +(n-1) × 4
= 4n -1
Hence, the nth term of the AP is (4n -1).
संबंधित प्रश्न
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