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3 years ago

Find the first six terms of the sequence. a1 = -8, an = 5 • an-1

1 answer:

5 0

$a_1 = -8\\
a_n = 5 \cdot a_{n-1 }\\\\
a_2=5\cdot(-8)=-40\\
a_3=5\cdot(-40)=-200\\
a_4=5\cdot(-200)=-1000\\
a_5=5\cdot(-1000)=-5000\\
a_6=5\cdot(-5000)=-25000$

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Find the sum of the first 47 terms of the following series, to the nearest integer.

Leokris [45]

Answer:

The sum of the first 47 terms of the series, 12, 16, 20, ... S₄₈ is 4,888

Step-by-step explanation:

The given series is;

12, 16, 20, ...,

Therefore, the first term of the series is, a = 12

The common difference of series is found as follows;

The difference between subsequent terms, 12 and 16 is 16 - 12 = 4

The difference between subsequent terms, 16, and 20 is 20 - 16 = 4

Therefore, the common difference, d = 4

The series is therefore an arithmetic projection, AP

The sum of the first 'n' terms of an AP, Sₙ, is given as follows;

$S_n = \dfrac{n}{2} \cdot \left [2 \cdot a + (n - 1)\cdot d \right ]$

(47/2)*(2*12+(47-1)*4)

The sum of the first 47 terms is therefore given as follows;

$S_n = \dfrac{47}{2} \cdot \left [2 \times 12 + (47 - 1)\times 4 \right ] = 4,888$

The sum of the first 47 terms of the series, 12, 16, 20, ... S₄₈ = 4,888

5 0

2 years ago

3/2000 as a decimal

Anarel [89]

Decimal

3/2000 = 0.0015

4 0

4 years ago

Pleaseeee helppp answer correctly !!!!!!!!!!!!! Will mark Brianliest !!!!!!!!!!!!!!!!

ohaa [14]

Answer: 132 degree

Step-by-step explanation:

X + 48 = 180

X = 180 - 48

X = 132 degree

5 0

3 years ago

The olympics are held every four years. In 2016, the XXXI olympiad were held in Rio de Janeiro,Brazil. Determine the year of the

Anna007 [38]

Answer:

First Olympic held in year 1896.

Step-by-step explanation:

Number of Olympiad held in Rio = XXXI = 31st

Difference of years in two consecutive Olympiads = 4 years

Number of years spent in 31 Olympiads can be calculated by,

Number of years spent = (n - 1)d

Here n = number of Olympiads held

d = difference between two consecutive Olympiads

Number of years spent till 31st Olympiads = (31 - 1)×4

= 120 years

Therefore, 1st Olympiad held in the year = 2016 - 120

= 1896

6 0

3 years ago

Multiply and give the answer in scientific notation:

kakasveta [241]

Step-by-step explanation:

given

$(1.5 \times {10}^{4} )(8 \times {10}^{8} )$

in order to make multiplication easier we need to change the 1.5 into a whole number form.

thus

$(15 \times {10}^{ - 1} \times {10}^{4} )(8 \times {10}^{8} )$

$= (15 \times {10}^{4 - 1} )(8 \times {10}^{8} )$

First law of indices applied there

=(15×10^3)(8×10^8)

=(15×8)(10^3×10^8)

=120×10^3+8 ( first law of indices, which states that , numbers of the same base multiplying each other, take one of the base and add the exponent. and clearly both 15 and 8 are in base 10

=120×10^11

=1.20×10^2 ×10^11

=1.20×10^11+2

=1.20×10^13

so the answer is alt B

7 0

3 years ago