geometric sequence

Question

find the missing term in this geometric sequence:

13,___,208

Answer 1

Note that in a geometric sequence, a common ratio (or factor) is multiplied to get the next number.

Let the common ratio be r.

so the sequence is 13, 13r, 13r²

So 13r² = 108. Now solve for r.

Divide both sides by 13.

r² = 16

r= +/-4.

So the middle number is 13*4=52 or 13*-4 = -52.