# Arithmetic and Geometric Progressions

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## Arithmetic Progression

a, b, c and d are in A.P., What can we say about terms bcd, acd, abd and abc?
1. They are also in A.P.
2. They are also in H.P.
3. They are also in G.P.
4. They are not in an A.P., G.P. or H.P.

Choice B. They are also in H.P.

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## Detailed Solution

a, b, c and d are in A.P.

Dividing through out this A.P. by abcd, we get

a/abcd , b/abcd , c/abcd , d/abcd are in A.P.

1/bcd , 1/acd , 1/abd , 1/abc are in A.P.

=> bcd, acd, abd and abc are in H.P.

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## More questions from Progressions

With some simple but very powerful ideas, one can cut down on a lot of working when it comes to progressions. For example, anchoring a progression around its middle term can be very useful. Reinforce these ideas with these questions.