The 17th term of an ap is 5 more than twice its 8th term. if the 11th term of the ap is 43, find the th n term.
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The 17th term of an ap is 5 more than twice its 8th term
a₁₇ = 5 + 2(a₈)
a + 16d = 5 + 2(a+7d)
a + 16d = 5 + 2a + 14d
16d - 14d = 2a - a + 5
2d = a + 5
a = 2d - 5
11th term of AP = 43
a₁₁ = a + 10d = 43
2d - 5 + 10d = 43
12d - 5 = 43
12d = 43+5
12d = 48
d = 48/12
d = 4
a = 2d - 5 = 2(4) - 5 = 8 - 5 = 3
∴ a = 3 and d = 4
nth term of AP = a + (n-1)d
= 3 + (n-1)(4)
= 3 + 4n - 4
= 4n - 1
a₁₇ = 5 + 2(a₈)
a + 16d = 5 + 2(a+7d)
a + 16d = 5 + 2a + 14d
16d - 14d = 2a - a + 5
2d = a + 5
a = 2d - 5
11th term of AP = 43
a₁₁ = a + 10d = 43
2d - 5 + 10d = 43
12d - 5 = 43
12d = 43+5
12d = 48
d = 48/12
d = 4
a = 2d - 5 = 2(4) - 5 = 8 - 5 = 3
∴ a = 3 and d = 4
nth term of AP = a + (n-1)d
= 3 + (n-1)(4)
= 3 + 4n - 4
= 4n - 1
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