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Ganezh [65]
1 year ago
10

Find the sum of the first 20 terms of an arithmetic sequence with an 18th term of 8.1 and a common difference of 0.25.

Mathematics
1 answer:
il63 [147K]1 year ago
8 0

The sum of the first 20 terms of an arithmetic sequence with the 18th term of 8.1 and a common difference of 0.25 is 124.5

Given,

18th term of an arithmetic sequence = 8.1

Common difference = d = 0.25.

<h3>What is an arithmetic sequence?</h3>

The sequence in which the difference between the consecutive term is constant.

The nth term is denoted by:

a_n = a + ( n - 1 ) d

The sum of an arithmetic sequence:

S_n = n/2 [ 2a + ( n - 1 ) d ]

Find the 18th term of the sequence.

18th term = 8.1

d = 0.25

8.1 = a + ( 18 - 1 ) 0.25

8.1 = a + 17 x 0.25

8.1 = a + 4.25

a = 8.1 - 4.25

a = 3.85

Find the sum of 20 terms.

S_20 = 20 / 2 [ 2 x 3.85 + ( 20 - 1 ) 0.25 ]

         = 10 [ 7.7 + 19 x 0.25 ]

         = 10 [ 7.7 + 4.75 ]

         = 10 x 12.45

         = 124.5

Thus the sum of the first 20 terms of an arithmetic sequence with the 18th term of 8.1 and a common difference of 0.25 is 124.5

Learn more about arithmetic sequence here:

brainly.com/question/25749583

#SPJ1

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Question 4 options: Find the mean and standard deviation for a binomial distribution with 680 trials and a probability of succes
lys-0071 [83]

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Mean for a binomial distribution = 374

Standard deviation for a binomial distribution = 12.97

Step-by-step explanation:

We are given a binomial distribution with 680 trials and a probability of success of 0.55.

The above situation can be represented through Binomial distribution;

P(X=r) = \binom{n}{r}p^{r} (1-p)^{n-r} ; x = 0,1,2,3,.....

where, n = number of trials (samples) taken = 680 trials

            r = number of success  

           p = probability of success which in our question is 0.55

So, it means X <em>~ </em>Binom(n=680, p=0.55)

<em><u>Now, we have to find the mean and standard deviation of the given binomial distribution.</u></em>

  • Mean of Binomial Distribution is given by;

                    E(X) = n \times p

       So, E(X) = 680 \times 0.55 = 374

  • Standard deviation of Binomial Distribution is given by;

                   S.D.(X) = \sqrt{n \times p \times (1-p)}

                               = \sqrt{680 \times 0.55 \times (1-0.55)}

                               = \sqrt{680 \times 0.55 \times 0.45} = 12.97

Therefore, Mean and standard deviation for binomial distribution is 374 and 12.97 respectively.

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3 years ago
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