Question

The 11th term of an arithmetic sequence is 57 and the sum of the first and fourth terms is 29. A) Determine the first three terms of the sequence​

Answer 1

Explanation:

Let's call the common difference of the arithmetic sequence "d", and the first term of the sequence "a". Then we can write two equations based on the information given:

a + 3d = 57 (the 11th term is 57)

a + a + 3d = 29 (the sum of the first and fourth terms is 29)

Solving for the first equation for "a", we get:

a = 57 - 3d

Substituting this expression for "a" into the second equation, we get:

57 - 3d + 3d = 29

57 = 29

So the first three terms of the arithmetic sequence are:

a = 57 - 3d

a + d = 57 - 2d

a + 2d = 57 - d

Solving for "d", we can find the value of "a", and then use the equations above to find the first three terms of the sequence