Geometric Sequences Riddle With Negative Ratios

Start with Classify Sequences With Negative Terms, then move to the arithmetic and geometric sheets. Use the mazes, the card sort and the riddle as self-checking review, and finish with Sequences as Functions Review.

Find the next term of 12 geometric sequences with negative ratios to solve a riddle about fish and money. The directions on the page read: Find the next term of each geometric sequence and write it on the line. Find that term in the bank and write its letter in the box. Read the letters from 1 to 12 to answer the riddle. The page opens with a worked example, and an answer key is included.

Yes, both. We made it for 8th grade algebra, and it works the same at home or at school. At home, a student can work through it alone and then go over it with you, which shows quickly what is solid and what needs another look. In class it works as independent practice, homework or a warm-up, and you can print one copy or a full set.

Subtract each term from the next one. If the difference is always the same, the sequence is arithmetic. If dividing each term by the one before gives the same number, it is geometric. A list like 1/4, 1/5, 1/6, 1/7 passes neither test.

Yes. A negative ratio makes the signs alternate, so −3, 12, −48, 192 has r = −4. Geometric Sequences With Negative Ratios has 16 lists like this.

Use first term + (n − 1) × d. For 52, 43, 34, 25, the 50th term is 52 + 49 × (−9) = −389. Find the 50th and 100th Terms practices this on 8 sequences.

Find d or r from two known terms, then work forward or backward. In 19, blank, −3, the change is −22 over two steps, so d = −11 and the missing term is 8.