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There are four arithmetic means between 2 and -18. The means a

Question

There are four arithmetic means between $2$ and $- 18.$ The means are

- 4, - 7, - 10. - 13

1, - 4, - 7, - 10

- 2, - 5, - 9, - 13

- 2, - 6, - 10, - 14

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Sebastian Discussed

There are four arithmetic means between

2

and

- 18.

The means are

12 mins ago

Discuss this question LIVE

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Text solutionVerified

Let the mean be

X_{1}, X_{2}, X_{3}, X_{4}

and the common difference be

b

; then

2, X_{1}, X_{2}, X_{3}, X_{4}, - 18

are in A.P.;

\Rightarrow - 18 = 2 + 5 b \Rightarrow 5 b = - 20 \Rightarrow b = - 4

Hence,

X_{1} = 2 + b = 2 + (- 4) = - 2; X_{2} = 2 + 2 b = 2 - 8 = - 6

X_{3} = 2 + 3 b = 2 - 12 = - 10; X_{4} = 2 + 4 b = 2 - 16 = - 14

The required means are

- 2, - 6, - 10, - 14

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Question Text	There are four arithmetic means between $2$ and $- 18.$ The means are
Answer Type	Text solution:1
Upvotes	154