Jambmaths question:
The sixth term of arithmetic progression is half of its twelfth term. The first term is equal to
Option A:
zero
Option B:
half of the common difference
Option C:
double the common difference
Option D:
the common difference
Jamb Maths Solution:
$\begin{align} & {{T}_{n}}=a+(n-1)d \\ & {{T}_{6}}=a+5d----(i) \\ & {{T}_{12}}=a+11d---(ii) \\ & {{T}_{6}}=\tfrac{1}{2}{{T}_{12}} \\ & a+5d=\tfrac{1}{2}(a+11d) \\ & 2a+10d=a+11d \\ & 2a-a=11d-10d \\ & a=d \\ & \text{The first term is equal to the common difference} \\\end{align}$
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