Find the missing terms in each arithmetic sequence

Question

3,_,_,_59.... An= A1 + (n-1) d

-4,_,_23... An= A1 + (n-1) d

Answer 1

1.) 3,_,_,_59.... An= A1 + (n-1) d

We will use the fifth term, 59 to solve the equation. We will substitute in 3 and 59 for A1 and An, respectively, and solve for d, the common difference.

59 = 3 + (5-1)d

56 = 4d

14 = d

To solve the remaining three terms, we can either add 14 to each successiveterm or use the equation. Either way, the terms will be: 17, 31, 45.

2.) -4,_,_23... An= A1 + (n-1) d

We will use the same approach. 23 will be the 4th term so n will be 4; A1 will be -4, and An will be 23.

23 = -4 + (4-1)d

27 = 3d

9 = d

To solve the two terms, we will could add 9 to each successive term or use the equation. Either way, the terms will be: 5 and 14.,

Answer 2

59 = 3 + 4d => 4d = 56 and d=14

23 = -4 + 3d => 3d = 27 and d = 9

Answer 3

3 + 4d = 59 => d = 14

-4 + 3d = 23 => 3d = 27 and d = 9