Question

What is the sum of the geometric sequence 1, -4, 16, if there are 7 terms?

Answer 1

find the next 4 terms and add them all up

Answer 2

or, recall the formula for a geometric series ....

Answer 3

The problem is I Dont understand how to do this, can u explain it to me ?

Answer 4

well, a geometric series is one in which each new term is created by multipying the last one by some constant value ...

1, times what, is -4?

Answer 5

-4

Answer 6

good; and -4, times -4 is 16 so this creates the sequence we are looking for

1
-4
16
16*(-4)
16*(-4)*(-4)
16*(-4)*(-4)*(-4)
16*(-4)*(-4)*(-4)*(-4)

those will be the first 7 terms, add them up

Answer 7

otherwise, you would have to remember yet another formula ...

1 - r^n
a * -------; a = first term, r = common ration, n=number of terms
1 - r

Answer 8

Im Trying to add them up

Answer 9

It gives me 3405

Answer 10

close ... 3277 should be it

Answer 11

Aw Okay , Thankx

Answer 12

spose we have a geometric sequence: a, ar, ar^2, ar^3, ..., ar^n

the sum of this sequence is: S= ar^0 + ar^1 + ar^2 + ar^3 + ... + ar^(n-1)

multiply by r again we get: rS = ar^1 + ar^2 + ar^3 + ar^4 + ... + ar^n

subtracting these we get:

S = ar^0 + ar + ar^2 + ar^3 + ... + ar^(n-1)
-rS = - ar - ar^2 - ar^3 - ... - ar^(n-1) - ar^n
-----------------------------------------------
(1-r)S = a + 0 + 0 + 0 + ... + 0 - ar^n


divide boths sides by 1-r

S = (a - ar^n))/(1-r)

factor out the a to get: S = a (1-r^n)/(1-r) for the formula

Answer 13

Oh

Answer 14

:) its fun to remember the math behind the formula ... just in case you forget the formula itself