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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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