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## Arithmetic Progressions

What's the sum of the first 100 positive integers? How about the first 1000? Learn the fun and fast way to solve problems like this. See more

# Warmup

If $$9, b, c, 18$$ is an arithmetic progression, what is the value of $$c?$$

True or false?

If $$(A, B, C, D,...)$$ and $$(a, b, c, d,...)$$ are both arithmetic progressions, then $$(A-a, B-b, C-c, D-d, ...)$$ is guaranteed to also be an arithmetic progression.

Jaspreet had $5 in her account on Day 1. On each subsequent day after Day 1, she deposited a constant amount into her account. At the end of Day 101, she has$305.

How many dollars did she have in her account at the end of Day 3?

Suppose $$a, b, c, d, ...$$ is an arithmetic progression with $$b = 8.$$ What is the average (arithmetic mean) of $$a, b,$$ and $$c?$$

$5,9,a,b,c,...$

If this sequence is an arithmetic progression, what is the value of $$c?$$

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