Question 19


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Jambmaths question: 

The sixth term of arithmetic progression is half of its twelfth term. The first term is equal to

Option A: 


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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