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3 years ago

Find the common diffirence in the arithmetic sequence 1, 6/4, 10/4, 3...

Mathematics

1 answer:

Temka [501]3 years ago

8 0

Answer:

See explanation

Step-by-step explanation:

6/4 = 1.5

10/4 = 2.5

Therefore the sequence is 1, 1.5, 2.5, 3

So the common difference is either 0.5 or 1

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$\huge\boxed{14\ \text{and}\ 7}$

Step-by-step explanation:

$n,\ m-\text{positive integer}\\\\n=2m-\text{a positive integer is twice another}\\\\\dfrac{1}{n}+\dfrac{1}{m}=\dfrac{3}{14}-\text{the sum of the reciprocal of the two positive integer is }\ \dfrac{3}{14}\\\\\text{We have the system of equations:}\\\\\left\{\begin{array}{ccc}n=2m&(1)\\\dfrac{1}{n}+\dfrac{1}{m}=\dfrac{3}{14}&(2)\end{array}\right$

$\text{Substitute (1) to (2):}\\\\\dfrac{1}{2m}+\dfrac{1}{m}=\dfrac{3}{14}\\\\\dfrac{1}{2m}+\dfrac{1\cdot2}{m\cdot2}=\dfrac{3}{14}\\\\\dfrac{1}{2m}+\dfrac{2}{2m}=\dfrac{3}{14}\\\\\dfrac{1+2}{2m}=\dfrac{3}{14}\\\\\dfrac{3}{2m}=\dfrac{3}{14}\Rightarrow2m=14\qquad\text{divide both sides by 2}\\\\\dfrac{2m}{2}=\dfrac{14}{2}\\\\\boxed{m=7}$

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Find the common diffirence in the arithmetic sequence 1, 6/4, 10/4, 3...​

Find the common diffirence in the arithmetic sequence 1, 6/4, 10/4, 3...