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2 years ago

(A) If the 13th and 38th terms of an arithmetic sequence are -53 and -128,

Mathematics

1 answer:

grigory [225]2 years ago

7 0

9514 1404 393

Answer:

(A) -2018

(B) 5/36

Step-by-step explanation:

(A) The rate of change between any pair of terms in an arithmetic sequence is the same:

(a668 -a38)/(668 -38) = (a38 -a13)/(38 -13)

a668/630 = a38/630 +(a38 -a13)/25 . . . . add a38/630 to both sides

a668 = a38 +630/25(a38 -a13) = -128 +25.2(-128 -(-53)) = -128 -1890

a668 = -2018

(B) The sum of an infinite geometric series is ...

S = a1/(1 -r) . . . . . . for first term a1 and common ratio r

We are given S = 6, a1 = 5, so we can find r to be ...

6 = 5/(1 -r)

1 -r = 5/6

1 -5/6 = r = 1/6

Then the 3rd term is ...

a3 = 5×(1/6)^(3 -1) = 5/36

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Given the figure below, find the values of x and z.

aleksandrvk [35]

Answer: x = 2 and z=78

Step-by-step explanation:

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3 years ago

-4b - 5 + 2b =10. Can I have some help solving this.

kramer

Answer:

-7.5

Step-by-step explanation:

Simplify

-4b - 5 + 2b = 10

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3 years ago

Read 2 more answers

Suppose that 10 years ago you bought a home for $160,000, paying 10% as a down payment, and financing the rest at 9% interest fo

Goshia [24]

Answer:

Current monthly payment on their existing mortgage would be $1158.66

Step-by-step explanation:

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Down payment = 10% of 160,000

Down Payment = $16,000

Balance amount = 160,000 - 16,000 = $144,000

Monthly payment formula:

$P=\dfrac{r(PV)}{1-(1+r)^{-n}}$

where,

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n is number of period, n=30x12 = 360

$P=\dfrac{0.0075\times 144000}{1-(1+0.0075)^{-360}}$

$P=\$ 1158.66$

Monthly payment would be same for 30 years.

Thus, Current monthly payment on their existing mortgage would be $1158.66

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2 years ago

A leaky faucet in kali's house drips water at a rate of 42 gallons per week. How many gallons does the faucet drip in three days

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Amount of water that the faucet leaks in 1 week = 42 gallons

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So it can said from the above deduction that the amount of water leaked by the faucet in Kali's house is 18 gallons.

hope this help .-.

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3 years ago

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