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2 years ago

The first term of an AP is -7 and the ratio of the eight term to the third term is 7:1 calculate the common difference

Mathematics

1 answer:

alukav5142 [94]2 years ago

4 0

Answer:

the common difference is 6.

Step-by-step explanation:

Given;

first term of an AP, a = -7

let the common difference = d

The third term is written as;

T₃ = a + 2d

The eight term is written as;

T₈ = a + 7d

The ratio of the eight term to third term = 7:1

$\frac{T_8}{T_3} = \frac{7}{1} = \frac{a+ 7d}{a + 2d} \\\\7 = \frac{a+ 7d}{a + 2d}\\\\Recall, a = -7\\\\7 = \frac{-7+ 7d}{-7 + 2d}\\\\7(-7 + 2d) = -7+ 7d\\\\-49 + 14d = -7 + 7d\\\\14d -7d = -7 + 49\\\\7d = 42\\\\d = \frac{42}{7} \\\\d = 6$

Therefore, the common difference is 6.

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3 years ago

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Step-by-step explanation:

Given

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Required

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2 years ago

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natali 33 [55]

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Step-by-step explanation:

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3 years ago

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3 years ago

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$x-2y=5 \\
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\hbox{solve the first equation for x:} \\
x-2y=5 \ \ \ |+2y \\
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\hbox{substitute 2y+5 for x in the second equation:} \\
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2 years ago