Question 44

Jambmaths question: 

If the term of an AP is twice the third term and the sum of first terms is 42, find the common difference.

Option A: 

1

Option B: 

2

Option C: 

3

Option D: 

6

Jamb Maths Solution: 

\[\begin{align}  & {{T}_{n}}=a+(n-1)d \\ & {{T}_{7}}=a+6d \\ & {{T}_{3}}=a+2d \\ & {{T}_{7}}=2{{T}_{3}} \\ & a+6d=2[a+2d] \\ & a-2d=0----(i) \\ & {{\text{S}}_{n}}=\tfrac{n}{2}\left[ 2a+(n-1)d \right] \\ & {{S}_{4}}=\tfrac{4}{2}\left[ 2a+3d \right]=42 \\ & 2(2a+3d)=42 \\ & 2a+3d=21----(ii) \\ & \text{from (i) }a=2d \\ & \text{Substitute }2d\text{ for }a\text{ in equation }(ii) \\ & 2(2d)+3d=21----(ii) \\ & 4d+3d=21 \\ & 7d=21;\text{   }d=3 \\\end{align}\]

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