Question

find first 15 term of geometric sequence of 4,12,36,108

Answer 1

Can you figure out the common ratio of the geometric series?

Answer 2

no

Answer 3

This is how a geometric series is formed.
You start with the first number. Here it is 4.
You multiply the first number by another number called the common ratio to get the second number.
You multiply the second number by the common ratio to get the third number.
And so on and so forth.
So the first number 4 was multiplied by some number (call it r) to get the second number which is 12.
Can you tell me what r is?

Answer 4

3

Answer 5

Yes. The common ratio = 3.
First number = 4
Second number = 4 x 3 = 12
Third number = 12 x 3 = 36
Fourth Number = 36 x 3 = 108
Fifth Number = ?

Answer 6

324?

Answer 7

Yes. Sixth Number = ?

Answer 8

972

Answer 9

Yes. Keep doing it until you get 15 numbers.
The geometric sequence so far are: 4, 12, 36, 108, 324, 972,
that covers 6 numbers and you have 9 more to go to get 15 numbers.

Answer 10

i think is 19,131,876

Answer 11

so will these be the sum of the 15 term?

Answer 12

No, not the sum. They want you to just list the first 15 terms. Not add them up.

Answer 13

what if they do?

Answer 14

oh ok i check they actually do ask for it

Answer 15

There is a standard formula for the sum of the first n terms of a geometric series. You can look it up in a text book or I can give it to you. You simply plug in the values into the formula to get the sum.
But here they simply want you to list all the 15 terms of the geometric series.
The number that you gave earlier, 19,131,876 is the 15th term of the series. So you have to list all the terms from 4, 12, 36, 108, 324, 972, ...., ...., ...., 19131876.
Also don't put commas in 19131876 because that will be confusing as the series has commas to separate each term.

Answer 16

can u give to me?

Answer 17

Sum = \[a \frac{ (r ^{n} - 1) }{(r - 1) }\]

where a is the first term in the geometric sequence; r is the common ratio; n is the number of terms in the geometric sequence.
Plug in the values for a, r and n and you will get the sum.

Answer 18

so is it 36?

Answer 19

You are getting sum = 36?

Answer 20

or is it the root 4374

Answer 21

No. The sum will be a very large number. Remember you yourself listed the 15th term in the sequence as: 19,131,876. So the sum of the first 15 terms will be even larger than that.

Answer 22

Substitute a = 4, r = 3, n = 15 in the formula for the sum.

Answer 23

I am getting sum = 28,697,814

Answer 24

ok can u solve this find A 250 when a1 = -50,d=5?

Answer 25

The problem is not typed correctly. Missing information.

Answer 26

use the formula of general term (the nth term) of arithmetic sequence to find the in dicated term of the sequence with the given first term, a1, and common difference, d
so find a250 when a1= -50, d=5

Answer 27

can u still help?

Answer 28

The nth term of an arithmetic sequence: a(n) = a(1) + (n-1)d
a(1) = -50, d = 5, n = 250
a(250) = -50 + (250 - 1)5 = -50 + 1245 = 1195.