The 3rd term of a geometric sequence is -2 and the 7th is -32. find the common ratio, the first term, the explicit formula, and the 10th term.

see explanation

Step-by-step explanation:

The n th term of a geometric sequence is

= a

where a is the first term and r the common ratio

Both a and r have to be found

Given a₃ = - 2, then

ar² = - 2 → (1)

Given a₇ = - 32, then

a = - 32 → (2)

Divide (2) by (1)

= , that is

= 16 ( take the fourth root of both sides )

r = 2 ← common ratio

Substitute r = 2 into (1)

a × 2² = - 2, that is

4a = - 2 ( divide both sides by 4 )

a = - ← first term

Hence

= - ← explicit formula

and

= - × = - 0.5 × 512 = - 256

the one below it is a function