Mathematics, 23.10.2019 18:00 jojo171717

3+ x, 9 + 3x, 13 + 4x, is an arithmetic sequence for some real number x.
b. find the 10th term of the sequence.

Answers: 3

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Answer from: autumnsumrall

The 10th term is 19

Step-by-step explanation:

For a sequence to be an arithmetic sequence, then there exist a common difference.

$\\$ How do we calculate common difference?

$\\$ Common difference is calculated by subtracting the first term from the second term, subtracting the second term from the third term and so on.

$\\$ From the sequence given , 3 + x, 9 + 3x, 13 + 4x, .. , calculating common difference implies

$\\$ (9+3x) – ( 3 +x) = 13 + 4x – ( 9 + 3x)

$\\$ Expanding, we have

$\\$ 9 + 3x – 3 – x = 13 + 4x – 9 – 3x

$\\$ ⇒9 – 3+3x –x = 13 – 9 +4x – 3x

$\\$ ⇒6 + 2x = 4 + x

$\\$ Collecting the like terms , we have

$\\$ 2x – x = 4 – 6

$\\$ which gives X = -2

$\\$ Since the value of x is gotten now , we can get what the given sequence looks like by substituting the value of x into each term given, the sequence becomes:

$\\$ 3 + (-2), 9 + 3(-2), 13 + 4(-2) +...

$\\$ Which gives

$\\$ 1 , 3 ,5, …

$\\$ We can therefore note that the common difference is 2

$\\$ check: 3 - 1 = 5 -3 = 2

$\\$ (b) To calculate the tenth term , we use the general formula for calculating nth term , which is given as

$\\$ $T_{n}$ = a + (n-1)d

$\\$ Where n is the number of terms , a is the first term and d is the common difference,

$\\$ Therefore, $T_{10}$ = 1 + ( 10-1)x2

$\\$ = 1 + 18

$\\$ = 19

Therefore the 10th term is 19

Answer from: Quest

unpaid balance is : $149.99-$50 = $99.99 new balance = 149.99+2.62-50 = $102.61 finance charge = 99.99- 0.21/12= $1.75 new balance = 99.99+1.75 = $101.74 average daily balance method average daily balance= 3399.70/30 = $113.32 finance charge = $ 0.21/12ă—113.32 = $1.98 new balance = $149.99-50+1.98 = $101.97

Answer from: Quest

Hello!

the answer is:

the correct option:

b. $x=2.23$

why?

to solve the problem, we need to remember how to operate to simplify exponential expressions using the logarithms.

we are given the equation:

$7^{x}=77$

then, using placing logarith with base 7 on both sides of the equation, we have:

$7^{x}=77log_{7}(7^{x})=log_{7}(77)x=log_{7}(77)x=2.2322$

so, rounding the obtained result to two decimal places (nearest hundreth), we have:

$x=2.23$

hence, we have that the correct option:

b. $x=2.23$

have a nice day!

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3+ x, 9 + 3x, 13 + 4x, is an arithmetic sequence for some real number x.
b. find the 10th te...