# Common Difference Problem

Pro Problems > Math > Algebra > Functions > Arithmetic Sequences## Common Difference Problem

The common difference in an arithmetic sequence is two more than the first term. The fourth term is 30. What is the first term?

## Solution

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### N and N + 1

The sum of the n^{th} term and the (n + 1)^{th} term of an arithmetic sequence is 62. The sum of the first and second terms is 14. The sum of the third and fourth terms is 22. Find n.

### Sequence by Threes

The sum of the first three terms of an arithmetic sequence is 72. The sum of the next three terms is 189. What is the sum of the next three terms after that?

### Odds and Evens

If you add the first five even numbered terms of an arithmetic sequence, the result is 27 more than if we had added the first five odd numbered terms. What is the common difference of the sequence?

### Sum of Squared Terms

The sum of the squares of the first two terms in an arithemetic sequence is 52. The common difference is 2. What are the possible values for the first term?

### Seventh Term

In an arithmetic sequence, the first term is twice the fourth term, and the second term is equal to 9 more than the sum of the fifth and sixth terms.

What is the seventh term of the sequence?

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