The 2nd term of a geometric sequence is 24, and the 5th term is 81. What is the 1st term? 

The 3rd term of an arithmetic sequence is 17, and the 9th term is 83. What is the 1st term? 

All terms in a geometric sequence are positive integers, and the first three terms are n, n + 3 and 2n + 6. What is the 4th term of this sequence?

The first three terms of an arithmetic sequence are p, 2p + 6 and 5p – 12. What is the 4th term of this sequence?

The 1st and 18th terms of an arithmetic sequence are 4 and 8.25, respectively. What is the 35th term of the sequence? Express your answer as a decimal to the nearest tenth.

What is the 10th term of the geometric sequence 729, 243, 81, 27, …? Express your answer as a common fraction.

What is the sum of the first 100 terms of the arithmetic sequence 3, 11, 19, 27, …?

What is the 100th term of the arithmetic sequence 3, 11, 19, 27, …?

For years, Mrs. Meany has had a tradition of giving her students a list of books from which they had to choose two to read during winter break. This year, Mrs. Meany added n book(s) to the list. If there are now 99 more ways that two books can be selected, what is the sum of all possible values of n?

One candle burns entirely in 6 hours, and another burns entirely in 9 hours. The candles were lit at the same time, and they were the same height when lit. After how many hours will one candle be half the height of the other? Express your answer as a decimal to the nearest tenth.

The mean of a set of five different positive integers is 21. How many values are possible for the median of this set of positive integers? 

What is the smallest positive integer that is greater than 100 and leaves a remainder of 1 when divided by 3, a remainder of 2 when divided by 5 and a remainder of 3 when divided by 7?

The three sides of a right triangle form a geometric progression. What is the ratio of the length
of the shortest side to the length of the hypotenuse? Express your answer as a decimal to the
nearest hundredth.

Suppose that the price of game tickets has gone up 4% every year for the past 25 years. What percent of today’s game ticket price is the price of a game ticket 13 years ago? Express your answer to the nearest whole number

Some students in a gym class are wearing blue jerseys, and the rest are wearing red jerseys. There are exactly 25 ways to pick a team of 3 players that includes at least 1 player wearing each color. How many students are in the class?

A 6-8-10 triangle is revolved about the side of length 10 units. What is the volume of the resulting solid? Express your answer as a decimal to the nearest tenth. 

A right triangle has integer side lengths a, b and c with a < b < c. If a + c = 49, what is the area of the triangle?

A club with 22 students is forming a committee of either 4 or 5 students. What is the ratio of the number of different 4-person committees possible to the number of different 5-person committees possible? Express your answer as a common fraction.

When written in a certain positive base b, 363 (base 10) is 123 (base b). What is the value of b?

A set of seven different positive integers has a mean of 13. What is the positive difference between the largest and smallest possible values of its median?