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Varvara68 [4.7K]
3 years ago
5

The first element in an arithmetic sequence is 2. Its twenty second is 14. Find the value of n so that a(n)=6

Mathematics
1 answer:
Aleks04 [339]3 years ago
8 0

Answer:

<h2>n = 8</h2>

Step-by-step explanation:

Given the nth term of an arithmetic sequence to be Tn = a+(n-1)d

a = first term of the sequence

n = number of terms

d = common difference.

Given the first element a = 2 and 22nd to be 14

T22 = a+(22-1)d = 14

a+21d = 14

Substtuting a = 2 into the equation to get d

2+21d = 14

21d = 12

d = 12/21

d = 4/7

The nth term of the sequence given a = 2 and d = 4/7 will be expressed as;

Tn = 2+(n-1)4/7

Given Tn = 6

6 = 2+(n-1)4/7

6 = 2+4/7 n - 4/7

6-2+4/7 = 4/7 n

32/7=4/7 n

32 = 4n

n = 32/4

n = 8

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Answer:

A) 22 cans required to paint

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Step-by-step explanation:

As we check the figure, we have a composite figure.

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B)

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Including tax of 13% = $561 + $561 \times \frac{13}{100} = $561 + $72.93 = <em>$633.93</em>

<em></em>

So, the answers are:

A) <em>22 cans </em>required to paint

B) Including 13% tax, cost of painting =<em> $633.93</em>

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