In the sequence S, the difference between any two consecutive terms is equal. If the sum of the fourth term and the fifth term of the sequence is equal to the seventh term of the sequence, what is the value of the second term of the sequence?
Answer Choices
Correct answer marked belowSee the full step-by-step explanation
You can see the correct answer above. Sign in for free to unlock the complete worked solution.
Track your performance and improve
Get detailed analytics, unlock full explanations, and move up difficulty tiers as you practice.
Unlock the full explanation
Create a free account to reveal the correct answer, see the step-by-step explanation, and start tracking your GMAT progress.
This one looked like it needed a ton of algebra but the d's cancel out really nicely. Key is just writing everything as a1 + something*d.
Right, I set a4 = x and it got messy fast, then switched to first term + d and it clicked.
Same here, once you see the d terms cancel it's basically a free point.
Wait, why does the answer not depend on the common difference at all? That part threw me off.
Because both sides end up having the same d, so it drops out and you're left with just the first term.
Got 8 but honestly took me longer than it should have. Easy to overthink when they give you so few numbers.
Haha same, I stared at it for a minute before just writing the terms out.
Solid 600-650 level question. Tests whether you can translate the word problem into a4 + a5 = a7 without panicking.
Agreed, the translation part is the whole question, the rest is trivial.
What it tests
Your ability to spot and extend arithmetic and geometric sequences and work with recursive definitions.
Common trap
Off-by-one errors in indexing (a₀ vs a₁) or confusing an arithmetic difference with a geometric ratio.