Determine the nth term of the AP whose 7th term is - 1 and 16th term is 17.
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siddhartharao77:
a = -13
Answered by
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We know that nth term of an AP is an = a + (n - 1) * d
(i)
Given that 7th term of an AP is -1.
⇒ a7 = a + (7 - 1) * d
⇒ -1 = a + 6d ------ (1)
(ii)
Given that 16th term of AP is 17.
⇒ a16 = a + (16 - 1) * d
⇒ 17 = a + 15d ------ (2)
On solving (1) & (2), we get
⇒ a + 6d = -1
⇒ a + 15d = 17
-----------------
-9d = -18
d = 2.
Substitute d = 2 in (1), we get
⇒ a + 6d = -1
⇒ a + 6(2) = -1
⇒ a + 12 = -1
⇒ a = -13.
Now,
⇒ nth term of the AP an = a + (n - 1) * d
= -13 + (n - 1) * 2
= -13 + 2n - 2
= 2n - 15.
Therefore, nth term of the AP = 2n - 15.
Hope this helps!
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