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Question
Which term of the A.P. `18, 15(1)/(2)`, 13, ... is – 47?
Solution
`18, 15(1)/(2)`, 13, ... is – 47
Let nth term is –47
a = 18, d = `15(1)/(2) - 18 = -2(1)/(2) = (-5)/(2)`
∴ –47 = a + (n – 1)d
⇒ –47 = `18 + (n - 1)((-5)/2)`
⇒ –47 – 18 = `(-5)/(2)n + (5)/(2)`
⇒ `-65 – (5)/(2) = (-5)/(2)n`
⇒ `(-135)/(2) = (-5)/(2)n`
∴ n = `(-135)/(2) xx (2)/(-5)` = 27
∴ –47 is 27th term.
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