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?

Hi69420 May 12, 2024

#1**+1 **

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

CoolBird2006 May 12, 2024