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3 years ago

The first term of an Ap are x, 2x +1, and 5x+1 Find x and the sum of the l0 terms first

Mathematics

1 answer:

bazaltina [42]3 years ago

7 0

Answer:

145/2

Step-by-step explanation:

d=[2x+1-x] = [5x+1 -(2x+1)]

x+1=3x

x-3x=-1

-2x=-1

x=1/2

therefore first term is 1/2

second term is 2(1/2)+1= 2

common difference d is 2-1/2=3/2

sum of first n terms is n/2 [2a+(n-1)d] where n=10

sum of first 10 terms= 10/2[2×1/2+(10-1)3/2]

=5[1+(9)3/2] =5[1+27/2] = 5[29/2] =145/2

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The location of the 6th score relative to the mean is 5 points below the mean

Let:

$\bar x \to$ Mean

$a \to$ 5 scores

$b \to$ 6th scores

Given that:

$n = 6$

The 5 scores that are 1 above the mean implies that:

$a = \bar x + 1$

The mean of a dataset is calculated using:

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So, we have:

$\bar x =\frac{5a + b}{6}$

$\bar x =\frac{5(\bar x + 1) + b}{6}$

Open brackets

$\bar x =\frac{5\bar x + 5 + b}{6}$

Multiply both sides by 6

$6\bar x =5\bar x + 5 + b$

Make b the subject

$b = 6\bar x -5\bar x - 5$

$b = \bar x - 5$

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