Question

Simple Arithmetic Sequence:

What are the missing terms of the arithmetic sequence, 4, _, 14, _, 24, _?

I figured out that this sequence has a common difference of 5, meaning the blank parts should be 9, 19, and 29, but I don't believe I did it the proper/correct way. I just used common sense. No formulas. How would I do it the right way?

Answer 1

For questions like these, you don't really need a specific formula. Just go with whatever makes sense and hope for the best. It seems to be it is plus 5 each time so it should be 4,9,14,19,24,29

Answer 2

But if I were to use a formula, how would I derive it?

Answer 3

let say, 4 is the first number, namely a1, ok?

Answer 4

Right.

Answer 5

so, the first blank is the second number, namely a2, ok?

Answer 6

Yes.

Answer 7

It is an Arithmetic Sequence, hence , a2 = a1 + d, ok?

Answer 8

Ok.

Answer 9

now a3 =14, right?

Answer 10

Yes.

Answer 11

and a3 = a2 +d, right?

Answer 12

Right.

Answer 13

you have a2 = a1 + d
then a3 = a2 + d, so a3 = a1 + 2d , right?

Answer 14

Yes.

Answer 15

that is 14 = 4 +2d, right?

Answer 16

I see where you're getting at now. Isolate the d.

Answer 17

10 =2 d

Answer 18

Bingo, you can handle it from now. glad to see.

Answer 19

Divided by 2 = 5

Answer 20

Thank you. Makes sense. :-)

Answer 21

ok