Mean & Median of Arithmetic Sequences on SATs/Standardized Tests - The BIG IDEA!

Here are two standardized type questions that students sometimes struggle with. Those who do well on these kinds of questions know the key is to understand the basics of arithmetic sequences. The 2nd question is a bit more sophisticated. What changes did I make to complicate the picture?


1. The median of a set of 20 consecutive integers is 14.5. What is the mean of the first 10 of these?

2. The mean of 98 consecutive odd integers is 44. What is the greatest of these numbers?

Notes:
BIG IDEAS for ARITHMETIC SEQUENCES:
(a) MEAN = MEDIAN!
(b) MEAN = MEDIAN = (LAST + FIRST)/2
(c) N = (L-F)/D + 1
Can you guess what these variables represent?
Hint: This is a variation on a well-known formula for arithmetic sequences.