Two APs have the same common difference. The first term of one of these is $-1$ and that of the other is $-8$. Then the difference between their $4^{\text{th}}$ terms is:
$-1$
$-8$
$7$
$-9$
Step-by-Step Solution
Key Concept: The difference between any corresponding $n^{\text{th}}$ terms of two APs with the same common difference is constant and equal to the difference of their first terms.
Stepwise Solution:
Let first AP have $a = -1$, second have $a' = -8$. Both have common difference $d$. [0.5 Mark]
$a_4 - a'_4 = (-1 + 3d) - (-8 + 3d) = -1 + 8 = 7$. [0.5 Mark]
Marking Scheme:
• Writing 4th term expressions: 0.5 Mark
• Finding difference $= 7$: 0.5 Mark
Correct Answer: $7$