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navik [9.2K]
3 years ago
15

Find the 7th term of a geometric sequence with t1 = 6 and r = 4.

Mathematics
2 answers:
Helen [10]3 years ago
8 0

To solve for the 7th term of a geometric sequence with t1 = 6 and r = 4, we use the following equation:

<span>
a(n) = a(1) r^(n-1)
a7 = (6) 4^(7-1)
a7 = 24576</span>

Hope this answers the question. Have a nice day. Feel free to ask more questions.

Montano1993 [528]3 years ago
6 0

Answer:

24,576.

Step-by-step explanation:

We have been given that first term of a geometric sequence is 6 and common ratio is 4. We are asked to find the 7th term of the sequence.

We know that a geometric sequence is in form a_n=a_1\cdot r^{n-1}, where,

a_n = nth term of sequence,

a_1 = 1st term of sequence,

r = common ratio.

Upon substituting a_1=6 and r=4 and n=7 in geometric sequence formula, we will get:

a_7=6\cdot(4)^{7-1}

a_7=6\cdot(4)^{6}

a_7=6\cdot 4,096

a_7=24,576

Therefore, the 7th term of the given geometric sequence would be 24,576.

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Does any one know this i need help!!!
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3 years ago
Five lemons costs 1.80.What is the cost per lemon.At this rate ,what is the cost of mine lemons
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3 0
3 years ago
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4 0
3 years ago
There are nickels, dimes, quarters in a large piggy bank, for every 2 nickels there are 3 dimes, for every 2 dimes there are 5 q
Alex

There are 80 nickels and 120 dimes and 300 quarters in piggy bank

<em><u>Solution:</u></em>

Given that,

For every 2 nickels there are 3 dimes ,

So, ratio of nickel to dime will be 2 : 3

Also for every 2 dimes there are 5 quarters

So, ratio of dime to quarters is 2 : 5

Let us first find the ratio of nickles to dimes to quarters

nickel : dime = 2 : 3

dime : quarters = 2 : 5

\frac{nickel}{dime} = \frac{2}{3}

nickel = \frac{2}{3} dime

\frac{dime}{quarter} = \frac{2}{5}

quarter = \frac{5}{2}dime

So,

nickel : dime : quarter = \frac{2}{3}dime : dime : \frac{5}{2}dime\\\\nickel : dime : quarter = \frac{2}{3} : 1 : \frac{5}{2}\\\\nickel : dime : quarter = 4 : 6 : 15

Thus nickel : dime : quarters = 4 : 6 : 15

Now, let the number of nickel be 4x

Let the number of dimes be 6x

Let the number of quarters be 15x

From given question,

There are 500 coins in all.

number of nickel + number of dimes + number of quarters = 500

4x + 6x + 15x = 500

25x = 500

x = 20

Thus,

number of nickel = 4x = 4(20) = 80

number of dimes = 6x  = 6(20) = 120

number of quarters = 15x = 15(20) = 300

Thus there are 80 nickels and 120 dimes and 300 quarters in piggy bank    

3 0
3 years ago
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