Thread: Missing terms in arithmetic & geometric sequences.

Hello, I have no idea how to go about when finding, "missing terms." I would like to know how to at least start solving these type of problems. Many thanks in advance!

A. "Fill in the missing terms for each arithmetic sequence:"
1) 3, __,__,__,__,__,__,__,__,__, 75

2) __,__,__, -4, __,__,__,__,26


B. "Fill in the missing terms for each geometric sequence:"
1) 100,__,4

2) 2,__,__,__,162

Hello, Mulya66!

A. Fill in the missing terms for each arithmetic sequence.

You're expected to know the formula for the nth term of an arithmetic sequence:
. . . . an .= .a1 + (n-1)d
where a1 is the first term and d is the common difference.

1) .3, __, __, __, __, __, __, __, __, __, 75

We see that: .a1 = 3 .and .a11 = 75

Since .a11 .= .a1 + 10d
. . we have: .3 + 10d .= .75 . . → . . d = 7.2

The sequence is: .3, 10.2, 17.4, 24.6, 31.8, 39, 46.2, 53.4, 60.6, 67.8, 75

2) .__, __, __, -4, __, __, __, __, 26

We are given: .a4 = -4 .and .a9 = 26

So we have: .a1 + 3d .= .-4 . [1]
. - . . o . . . . a1 + 8d .= .26 ([2]

Subtract [1] from [2]: .5d = 30 . . → . . d = 6

Substitute into [1]: .a1 + 3·6 .= .-4 . . → . . a1 = -22

The sequence is: .-22, -16, -10, -4, 2, 8, 14, 20, 26

B. "Fill in the missing terms for each geometric sequence.

You're expected to know the formula for the nth term of a geometric sequence.
. . . . an .= .a1·r^{n-1}
where a1 is the first term and r is the common ratio.

1) . 100, __, 4

We are given: .a1 = 100 .and .a3 = 4

Then: .a3 .= .100·r² .= .4 . . → . . r = 1/5

The sequence is: .100, 20, 4

2) .2, __, __, __, 162

I'll let you work on this one . . .

Thank you so much.

Originally Posted by Soroban

Hello, Mulya66!

2, __,__,__,162

I'll let you work on this one . . .

Following your steps, I found that r = 3. Thus, the missing numbers are 6, 18, and 54. I'm proud of myself, thanks again. :-)