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The first term of an arithmetic sequence is 2. The sum of the third and the sixth terms is 25. What is the fourth term?

 May 12, 2024
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An arithmetic sequence has a common difference between each term

Let the common difference be n

The first term = 2

The second term = 2+n

The third term = 2+2n

The fourth term = 2+3n

The fifth term = 2+4n

The sixth term = 2+5n

And so on...

The sum of the third and sixth terms is 25 so:

2+2n+2+5n = 25

7n+4 = 25

7n = 21

n = 3

Thus, the fourth term is 2+3n = 2+9 = 11

 May 12, 2024

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