Find the common ratio of the geometric sequence 7, 28, 112,...

solvarmedw
2022-10-07
Answered

Find the common ratio of the geometric sequence 7, 28, 112,...

You can still ask an expert for help

recreerefr

Answered 2022-10-08
Author has **7** answers

The common ratio for this problem is 4.

The common ratio is a factor that when multiplied by the current term results in the next term.

First term: 7

$7\cdot 4=28$

Second term: 28

$28\cdot 4=112$

Third term: 112

$112\cdot 4=448$

Fourth term: 448

This geometric sequence can be further described by the equation:

$a}_{n}=7\cdot {4}^{n-1$

So if you want to find the 4th term , n=4

${a}_{4}=7\cdot {4}^{4-1}=7\cdot {4}^{3}=7\cdot 64=448$

Note:

$a}_{n}={a}_{1}{r}^{n-1$

where $a}_{1$ is the first term, $a}_{n$ is the actual value returned for a specific nth term and r is the common ratio.

The common ratio is a factor that when multiplied by the current term results in the next term.

First term: 7

$7\cdot 4=28$

Second term: 28

$28\cdot 4=112$

Third term: 112

$112\cdot 4=448$

Fourth term: 448

This geometric sequence can be further described by the equation:

$a}_{n}=7\cdot {4}^{n-1$

So if you want to find the 4th term , n=4

${a}_{4}=7\cdot {4}^{4-1}=7\cdot {4}^{3}=7\cdot 64=448$

Note:

$a}_{n}={a}_{1}{r}^{n-1$

where $a}_{1$ is the first term, $a}_{n$ is the actual value returned for a specific nth term and r is the common ratio.

asked 2022-06-26

An experiment is to flip a coin until you either get two heads in a row or two tails in a row. If that happens, you stop. Also, if you flip the coin four times without getting two in a row, you stop. Some possible sequences of flips are TT, THH and HTHT.

How many different sequences of flips are possible in this situation?

How many different sequences of flips are possible in this situation?

asked 2022-09-08

How do you find the first term of the arithmetic sequence given an = 48, Sn = 546, n = 26?

asked 2022-09-14

Find an arithmetic sequence with a common difference of -5

asked 2022-09-23

What is the missing sequence in $1\frac{3}{8},1\frac{3}{4},2\frac{1}{8}{,}_{\_},2\frac{7}{8}$?

asked 2021-05-14

The 4th term of an AP is 4 and the 8th term is 22 what is the 1st term?

asked 2022-10-23

Find the formula for $a}_{n$ for the arithmetic sequence ${a}_{1}=5,{a}_{4}=15$

asked 2022-09-05

An arithmetic series has a common difference of 7. Given that the sum of the first 20 terms of the series is 530, Please, help me with finding the first term of the series