Patterns & Sequences
Arithmetic and geometric sequences, pattern recognition, and nth-term formulas β classified under algebra because the core skill is generalizing a rule, even though SSAT places it under Number Concepts
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Have you ever noticed how a staircase goes up by the exact same height every step? Or how the number of zombies in your favorite video game doubles every level? π§ββοΈ Thatβs a pattern! Patterns and sequences are just lists of numbers that follow a secret rule. On the SSAT, your mission is to become a math detective and crack that secret code! π΅οΈββοΈ
There are two main types of number patterns youβll see. The first is an "arithmetic" (air-ith-MET-ic) sequence. This is like adding the same number of pepperoni slices to every new pizza you order. If the first pizza has 3 slices, the next has 5, and the next has 7, the secret rule is just .
The second type is a "geometric" sequence. This is when you multiply to get to the next number. Imagine a magical piggy bank where your money triples every day. If you start with 2 dollars, tomorrow you'll have 6, and the next day you'll have 18. The secret rule here is ! π·
Sometimes, patterns aren't just adding or multiplying. You might see a pattern hiding in fractions, where the top numbers (numerators) do one thing and the bottom numbers (denominators) do another. The trick to crushing these SSAT questions is to look at the first few numbers, guess the rule, and then test it to see if it works for the whole line. You've got this!
Practice Questions
4 practice questions for SSAT Middle Level
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- Let's find the numbers in the sequence step-by-step. The first number is 3 and the second is 4. The third number is . The fourth number is . The fifth number is .
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- The pattern consists of the 5 letters M, A, T, H, S repeating in that exact order. To find the 38th letter, divide 38 by 5. The quotient is 7 with a remainder of 3. This means the 5-letter pattern repeats 7 full times, accounting for 35 letters. The 36th letter starts the pattern again with M, the 37th is A, and the 38th is T.
In the sequence above, is the first term. For each term after the first, the numerator is 2 more than the preceding numerator, and the denominator is 3 more than the preceding denominator. What is the 7th term in the sequence?
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- We can find the terms by continuing the pattern of adding 2 to the numerator and 3 to the denominator. The first 4 terms are given: . The 5th term is . The 6th term is . The 7th term is .
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- The first term is 10. Subtracting 2 each time, the first six terms of the sequence are 10, 8, 6, 4, 2, and 0. The sum of these six terms is .
Tips & Strategies
- Always test your secret rule on the third number in the sequence. A rule might work for the first two numbers (like ), but fail on the next one (like ).
- If a sequence of fractions looks confusing, don't panic! Split it into two separate patterns: one for the top numbers (numerators) and one for the bottom numbers (denominators).
- For 'nth term' questions, you don't need to memorize complex formulas. Just plug into the answer choices and see which one gives you the very first number in the sequence!
Common Mistakes
- Watch out for assuming a pattern is addition when it's actually multiplication. Always check at least three numbers to confirm the pattern type!
- Don't forget that sequences can go backwards! If the numbers are getting smaller, your secret rule might be subtracting or dividing.
Frequently Asked Questions
What does 'nth term' mean on the SSAT?
It's just a mathy way of saying 'any number in the line'. The 'n' stands for the position of the number, so the 1st term is when , and the 100th term is when !
Will I have to find super huge numbers like the 50th term?
Sometimes! But don't worry, you won't have to count it out one by one. The SSAT will either give you a formula, or you can find the rule and plug in .
What if the numbers go up, then down, then up again?
That's an alternating sequence! It usually means there are two different patterns mixed together, or the rule involves multiplying by a negative number.
Can I use a calculator for these on the SSAT?
Nope! The SSAT doesn't allow calculators. But the good news is that the patterns will always be numbers you can easily add or multiply in your head or on your scratch paper.