Question

The first three terms of a geometric sequence are as follows.

−2, 10, −50

Find the next two terms of this sequence.
Give exact values (not decimal approximations).

Answer 1

Explanation:

in a geometric sequence every new term is created by multiplying the previous term by a constant factor. this factor is constant (= the same) for the whole sequence.

a1 = a1

a2 = a1 × f

a3 = a2 × f = a1 × f × f = a1 × f²

...

an = a1 × f^(n-1)

so, we have here

a1 = -2

a2 = a1 × f = -2 × f = 10

f = 10/-2 = -5

an = -2 × -5^(n-1)

in any case, the next 2 terms are

-50 × -5 = 250

250 × -5 = -1250