the 16th term of an AP is 1 more than twice its 8th term. If the 12th term of the AP is 47, then find its nth term.
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a16 = a + 15 d
a8 = a + 7 d
a + 15 d = 1 + 2 a + 14 d
d = a + 1
a12 = 47
a + 11 d = 47
d - 1 + 11 d = 47
12 d = 48
d = 4 ⇒ a = 3
an = a + (n-1) d = 3 + (n-1) 4 = 3 + 4 n - 4 = 4 n - 1
a8 = a + 7 d
a + 15 d = 1 + 2 a + 14 d
d = a + 1
a12 = 47
a + 11 d = 47
d - 1 + 11 d = 47
12 d = 48
d = 4 ⇒ a = 3
an = a + (n-1) d = 3 + (n-1) 4 = 3 + 4 n - 4 = 4 n - 1
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