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insert five arithmetic means between 25 and 4(with solution)​

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UK2019go

✏️ARITHMETIC MEANS

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[tex]\underline{\mathbb{PROBLEM:}}[/tex]

  • Insert five arithmetic means between 25 and 4.

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[tex]\underline{\mathbb{ANSWER:}}[/tex]

[tex]\quad\Large\rm» \:\: \green{21.5, 18, 14.5, 11\: and\: 7.5}[/tex]

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[tex]\underline{\mathbb{SOLUTION:}}[/tex]

- Let 25 would be the first term, the second, third, fourth, fifth and sixth term are the arithmetic means, and 4 would be the seventh term. Determine the common difference by using the formula.

[tex]\begin{aligned}&\bold{\color{lightblue}Formula:}\\&\boxed{d= \frac{a_n-a_k}{n - k}}\end{aligned} [/tex]

  • [tex]\begin{aligned}d= \frac{a_7-a_1}{7 - 1}\end{aligned} [/tex]

  • [tex]\begin{aligned}d= \frac{4-25}{7 - 1}\end{aligned} [/tex]

  • [tex]\begin{aligned}d= \frac{ \text - 21}{6}\end{aligned} [/tex]

  • [tex]d = \text - 3.5[/tex]

- Find the five arithmetic means.

  • [tex]a_2 = a_1 + d = 25 - 3.5 = 21.5[/tex]

  • [tex]a_3= a_2 + d = 21.5 - 3.5 = 18[/tex]

  • [tex]a_4= a_3 + d =18 - 3.5 = 14.5[/tex]

  • [tex]a_5= a_4+ d =14.5 - 3.5 = 11[/tex]

  • [tex]a_6= a_5+ d =11 - 3.5 = 7.5[/tex]

[tex]\therefore[/tex] The 5 arithmetic means between 25 and 4 is 21.5, 18, 14.5, 11, and 7.5.

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