Question

Show all work. find the missing terms of the arithmetic sequence... , 4, ?, ?, ?, 120, ...

Answer 1

Answer:

• -25, 4, 33, 62, 91, 120, ...

Step-by-step explanation:

Given

The arithmetic sequence

• .. , 4, ?, ?, ?, 120, ...

To find:

• Missing terms

Solution

Let the first term a₁ = x, and common difference = d then we have:

• a₁ = x
• a₂ = x + d = 4
• ...
• a₆ = x + 5d = 120

The difference of the 6th and  2nd terms:

• a₆ - a₂ =
• a + 5d - x - d = 120 - 4
• 4d = 116
• d = 116/4
• d = 29

Then we get the first term and other missing terms:

• x = 4 - 29 = -25
• a₁ = -25

-25, 4, 4+29 = 33, 33+29 = 62, 62 + 29= 91, 91+29 = 120, ...