Question

5,-10,20-40,...]
a15=

Answer 1

a15 = -163840

(Note: check if you really have to calculate the 15th term and not, say the 5th term in which case a5 = 80)

Explanation:

We have the sequence 5, -10, 20, -40,

We, see that for each term, the previous term is multiplied by -2,

so,

a1 = 5,

a2 = 5(-2) = -10

a3 = (-10)(-2) = 20

a4 = (20)(-2) = -40

and so on,

We see that this is a geometric sequence with -2 being the common ratio and 5 being a1,

so,using,

`a_(n) = a_1(r)^(n-1)\\a_n=5(-2)^(n-1)\\for \ n = 15,\\a_(15) = 5(-2)^(15)\\a_(15) = 5(-32768)\\a_(15) = -163840`

hence a15 = -163840