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Q: The fourth term of an AP is 15 and the sum of the first 5 terms is 55. Find the first term and the common difference?

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the first and fourth terms of a proportion are called the means ?

It is the "common difference".It is the "common difference".It is the "common difference".It is the "common difference".

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We need the common difference to accurately get the first term and then use it to find the sum of the first 20 terms.

An arithmetic sequence.

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There is no difference in the common usage of these terms.

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If the terms get bigger as you go along, the common difference is positive. If they get smaller, the common difference is negative and if they stay the same then the common difference is 0.

Not come across that!

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1 2 3 4 5 6 7 8 9 10 11 12 The common difference between consecutive terms is 1.

The terms are equivalent.

The sum of the first 12 terms of an arithmetic sequence is: sum = (n/2)(2a + (n - 1)d) = (12/2)(2a + (12 - 1)d) = 6(2a + 11d) = 12a + 66d where a is the first term and d is the common difference.

For an Arithmetic Progression, Sum = 15[a + 7d].{a = first term and d = common difference} For a Geometric Progression, Sum = a[1-r^15]/(r-1).{r = common ratio }.

First you factorise it. Then you cancel out the common terms.

It could be -3 or +3.

Very similar terms that in common parlance be used interchangeably.

The summation of a geometric series to infinity is equal to a/1-rwhere a is equal to the first term and r is equal to the common difference between the terms.

Depending on the context of the terms it might indeed display a difference. In common parlance however there would be no difference between them. Considering common and general to mean the same thing, there is no difference. Considering welfare not as "free stuff" but meaning the same as good then there is no difference.

Delaware was the first and Georgia was the fourth state to join the Union.

From the information given, all that can be said is that it will be a negative number.