Question

Which term of the A.P. ${\displaystyle 18,15\frac{1}{2}}$, 13, ... is – 47?

Answer 1

${\displaystyle 18,15\frac{1}{2}}$, 13, ... is – 47
Let nth term is –47
a = 18, d = ${\displaystyle 15\frac{1}{2}-18=-2\frac{1}{2}=\frac{-5}{2}}$
∴ –47 = a + (n – 1)d
⇒ –47 = ${\displaystyle 18+(n-1)\left(\frac{-5}{2}\right)}$

⇒ –47 – 18 = ${\displaystyle \frac{-5}{2}n+\frac{5}{2}}$

⇒ ${\displaystyle -65 –\frac{5}{2}=\frac{-5}{2}n}$

⇒ ${\displaystyle \frac{-135}{2}=\frac{-5}{2}n}$

∴ n = ${\displaystyle \frac{-135}{2}\times \frac{2}{-5}}$ = 27
∴  –47 is 27th term.