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Mariulka [41]
2 years ago
15

Two terms of an arithmetic sequence are a10=16 and a35=66 find the sum of the first 75 terms

Mathematics
1 answer:
andrew11 [14]2 years ago
4 0

The sum of the first 75 terms of the arithmetic sequence that has 10th term as 16 and the 35th term as 66 is 5400.  

<h3>How to find the sum of terms using Arithmetic sequence formula</h3>

aₙ = a + (n - 1)d

where

  • a = first term
  • d = common difference
  • n = number of terms

Therefore, let's find a and d

a₁₀ = a + (10 - 1)d

a₃₅ = a + (35 - 1)d

Hence,

16 = a + 9d

66 = a + 34d

25d = 50

d = 50 / 25

d = 2

16 - 9(2) = a

a = 16 - 18

a  = -2

Therefore, let's find the sum of 75 terms of the arithmetic sequence

Sₙ = n / 2 (2a + (n - 1)d)

S₇₅ = 75 / 2 (2(-2) + (75 - 1)2)

S₇₅ = 37.5 (-4 + 148)

S₇₅ = 37.5(144)

S₇₅ = 5400

learn more on arithmetic sequence here: brainly.com/question/1687271

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harkovskaia [24]

Answer:

=22%

Step-by-step explanation:

Since we have given two conditions simultaneously that is windy and not sunny. So we will use the concept of conditional probability.

The probability of sunny day= P(sunny)=10%

P(sunny)=10%=0.1

The probability of windy and not sunny=P(windy|not sun)=20%

P(windy|not sun)=20% = 0.2

Now divide the both probabilities:

P(windy|not sun)/P(sunny)

=0.2/[1-0.1]              

{Hence there are 10% chances of sun tomorrow than there are (1 - 0.1) chances of no sun}

If we subtract 1 from 0.1 than it becomes:

=0.2/0.9

=2/9

=0.2222222222

=22%

Hence the probability that it is windy = 22% ....

6 0
3 years ago
2 FOR 2.20 UNIT RATE
dlinn [17]

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5 0
2 years ago
Find the sum of the first 6 terms of 3 - 6 + 12 + …
Natalka [10]

Answer:

S_6 = -63

Step-by-step explanation:

The sequence above is a geometric sequence.

The common ratio (r) = \frac{-6}{3} = \frac{12}{-6} = -2

The common ratio < 1, therefore, the formula for the sum of nth terms of the sequence would be: S_n = \frac{a_1(1 - r^n)}{1 - r}

a1 = 3

r = -2

n = 6

Plug in the values into the formula

S_6 = \frac{3(1 - (-2^6)}{1 - (-2)}

S_6 = \frac{3(1 - (64)}{1 + 2}

S_6 = \frac{3(-63)}{3}

S_6 = -63

6 0
3 years ago
Please help quickly. Will mark brainlist!
rusak2 [61]

Answer:

A. 50.24

Step-by-step explanation:

C=2πr=2·π·8=50.24

4 0
2 years ago
Read 2 more answers
What is 3/4÷1/5? Plz show ur work...all help is appreciated
dangina [55]
3/4 ÷ 1/5
= 3/4 × 5/1
= 15/4

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3 0
3 years ago
Read 2 more answers
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