The 17th term of an A.P. is 5 more than twice its 8th term. If the 11th term of the A.P. is 43, find the nth term.
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Answer:
4n-1
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Nth term of the AP = 4n-1
Step-by-step explanation:
Given: 17th term of an A.P. is 5 more than twice its 8th term.
11th term of the A.P. is 43.
Find: the nth term.
Solution:
an = a +(n-1)d
a11 = 43
a + 10d = 43 -------(1)
a17 = 5 +a8
a + 16d = 5 + 2(a+ 7d)
a + 16d = 5 + 2a+ 14d
a -2d = -5 ------(2)
Subtracting (2) from (1), we get: +12d = 48
Therefore d = +4
Substituting d in (1), we get: a + 40 = 43
Therefore a = 3
Nth term of the AP = 3 + (n-1)4 = 3 + 4n - 4 = 4n-1
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