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2 years ago

The first term of an arithmetic sequence is 4 and the tenth term is 67.

Mathematics

1 answer:

Dmitry [639]2 years ago

6 0

Answer:

Step-by-step explanation:

Formula

tn = a1 + (n-1)* d

Givens

tn = 67 (it is the last term or the nth term

n = 10

a1 = 4

find d

Solution

67 = 4 + (10 - 1)*d

67 = 4 + 9*d Subtract 4 from both sides

67 - 4 = 9d

63 = 9d Divide by 9

63/9 = 9d/9

7 = d

Remark: This is a fundamental application of the arithmetic sequence. You pretty much have to know how to juggle it's parts.

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Firdavs [7]

Answer:

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Step-by-step explanation:

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3 years ago

How many solutions exist for the given equation?

sladkih [1.3K]

Answer:

Infinitely many

Step-by-step explanation:

12x + 1 = 3(4x + 1) - 2

12x + 1 = 12x + 3 - 2

12x + 1 = 12x + 1

Both sides are equal for all x, so infinite solutions

8 0

3 years ago

Read 2 more answers

55% of 387 is what number?

yarga [219]

Answer:

212.85

Step-by-step explanation:

55% = $\frac{55}{100}$ = 0.55

55% of 387 = 0.55 × 387 = 212.85

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3 years ago

Read 2 more answers

144 coins are divided equally among some children. If there were 3 children fewer, each child would have 16 coins. How many chil

enot [183]

Answer:

Step-by-step explanation:

144/16=9

Each child gets sixteen coins if there are nine children.

9+3=12

There are three more children so there are twelve.

8 0

3 years ago

I've tried to get the answer for this 13 times now (not joking), plzzz help: write a formula that represents the number of peopl

gtnhenbr [62]

Answer:

2820 seats
aₙ = 3n + 9

Step-by-step explanation:

This is an AP with:

The first term a₁ = 12
Common difference d = 3
Number of terms n = 40

Number of the seats:

Sₙ = 1/2*n(a₁ + aₙ) = 1/2n(2a₁ + (n - 1)d)
S₄₀ = 1/2*40(12*2 + 39*3) = 2820 seats

Formula of nth term:

aₙ = a₁ + (n - 1)d
aₙ = 12 + (n - 1)*3 = 12 + 3n - 3 = 3n + 9
aₙ = 3n + 9

6 0

3 years ago