LCAT Math, Algebra
Sequences for the LCAT: lesson and practice
In an arithmetic sequence you add the same number each time: an = a1 + (n − 1)d. In a geometric sequence you multiply by the same number: an = a1 · rn−1. The most common mistake is using n instead of n − 1.
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No calculator on the LCAT. LUMS’s official sample says calculators are not allowed, so every practice question here can be solved by hand.
| Type | nth term | Example |
|---|---|---|
| Arithmetic | a1 + (n − 1)d | 3, 1, −1, … 8th term: 3 + 7(−2) = −11 |
| Geometric | a1 · rn−1 | 2, 6, 18, … 5th term: 2 · 34 = 162 |
| Arithmetic sum | n(first + last) ÷ 2 | 1 + 2 + … + 10 = 10 × 11 ÷ 2 = 55 |
Common mistakes
Using n instead of n − 1From term 1 to term 8 there are 7 steps.
Losing the sign of d5, 2, −1 has d = −3.
Adding when you should multiply2, 6, 18 is geometric (× 3), not arithmetic.
Sample questions with answers
1. An arithmetic sequence has a₁ = 3 and d = −2. What is the 8th term?
- −11 (correct)
- −13
- −15
- −17
3 + 7(−2) = −11 (LUMS sample).
2. A geometric sequence starts at 2 with ratio 3. What is the 4th term?
- 54 (correct)
- 18
- 11
- 162
2 × 3³ = 54.
3. What is 1 + 2 + … + 20?
- 200
- 210 (correct)
- 400
- 420
20 × 21 ÷ 2 = 210.
Frequently asked questions
Are sequences on the LCAT?
Yes. LUMS’s official sample includes an arithmetic sequence question.
What is the formula for the nth term?
Arithmetic: a₁ + (n − 1)d. Geometric: a₁ · rⁿ⁻¹.
How do I find the sum of an arithmetic sequence?
Multiply the number of terms by the average of the first and last terms.