Respuesta :
the formula for a geometric sequence is an=a1×r^(n-1)
find r
let's use a2
15=-3×r^(2-1)
15=-3×r
divide both sides by -3
-5=r
This means each term is multiplied by -5 to get the next term (easier way of looking at it for this sequence)
ex..
a1: -3
a2: -3×-5=15
a3: 15×-5=-75
a4: -75×-5=375
let's find the next 3 terms
a5: 375×-5=-1875
a6: -1875×-5=9375
a7: 9375×-5=-46875
all 7 terms are
-3
15
-75
375
-1875
9375
-46875
now add them all up to get the answer
-3+15=12+-75=-63+375=312+-1875=-1563+9375=7812+-46875=
-39063 is the sum of the geometric sequense
find r
let's use a2
15=-3×r^(2-1)
15=-3×r
divide both sides by -3
-5=r
This means each term is multiplied by -5 to get the next term (easier way of looking at it for this sequence)
ex..
a1: -3
a2: -3×-5=15
a3: 15×-5=-75
a4: -75×-5=375
let's find the next 3 terms
a5: 375×-5=-1875
a6: -1875×-5=9375
a7: 9375×-5=-46875
all 7 terms are
-3
15
-75
375
-1875
9375
-46875
now add them all up to get the answer
-3+15=12+-75=-63+375=312+-1875=-1563+9375=7812+-46875=
-39063 is the sum of the geometric sequense
Geometric sequence is sequence where each term is same constant's multiple of previous term. The sum of given sequence is -66093
What is a geometric sequence and how to find its nth terms?
There are three parameters which differentiate between which geometric sequence we're talking about.
The first parameter is the initial value of the sequence.
The second parameter is the quantity by which we multiply previous term to get the next term.
The third parameter is the length of the sequence. It can be finite or infinite.
Suppose the initial term of a geometric sequence is [tex]a[/tex] and the term by which we multiply the previous term to get the next term is [tex]d[/tex]
Then the sequence would look like [tex]a, ad, ad^2, ...[/tex]
(till the terms to which it is defined)
Thus, the nth term of such sequence would be
[tex]T_n = ad^{n-2}[/tex]
What is the sum of a geometric sequence?
Lets suppose its
- initial term is [tex]a[/tex],
- multiplication factor is [tex]d[/tex] and
- let it has total n terms,
then, its sum is given as:
[tex]S_n = \dfrac{a(d^n-1)}{d-1}[/tex] (sum till nth term)
For the given sequence, it is visible that we have:
a = -3
d = 5 (as each term is multiplied by 5 to get the next term)
and n = 7(given)
Thus, its sum is
[tex]S_n = \dfrac{a(d^n-1)}{d-1}\\\\S_7 = \dfrac{-3 \times (5^7-1)}{5-1} = -66093[/tex]
Thus, The sum of given sequence is -66093
Learn more about geometric sequence here:
https://brainly.com/question/1607203
