Patrickdordas02idn
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Insert four arithmetic means between - 10 and 5​

Sagot :

UK2019idn

✏️ARITHMETIC MEAN

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Problem: Insert four arithmetic means between -10 and 5.

Solution: Let -10 be the first term. The second, third, fourth and fifth term will be the four arithmetic means. And 5 be the sixth term. Identify the common difference 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_6 - a_1 } {6 - 1}}\end{aligned}[/tex]

  • [tex]\begin{aligned}{d = \frac{5 - (\text - 10) } {6 - 1}}\end{aligned}[/tex]

  • [tex]\begin{aligned}{d = \frac{5 + 10} {6 - 1}}\end{aligned}[/tex]

  • [tex]\begin{aligned}{d = \frac{15} {5}}\end{aligned}[/tex]

  • [tex]d = 3[/tex]

- Find the four arithmetic means.

  • [tex]a_2 = a_1 + d = \text - 10 + 3 = \text - 7[/tex]

  • [tex]a_3 = a_2 + d = \text -7 + 3 = \text - 4[/tex]

  • [tex]a_4 = a_3 + d = \text -4 + 3 = \text -1[/tex]

  • [tex]a_5 = a_4 + d = \text -1 + 3 = \text 2[/tex]

- Therefore, the four arithmetic means are:

  • [tex] \large \boxed{ \sf \green{ \: \text - 7, \text - 4 , \text - 1 \: and \: 2 \: }}[/tex]

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