Question

insert three arithmetic means between - 5 and 7

Answer 1

Three arithmetic means between - 5 and 7 are -2, 1 and 4 .

Step-by-step explanation:

Given:

5 and 7.

To Find:

Three arithmetic means between - 5 and 7.

Formula Used:

nth term of the Arithmetic Progression (A.P) tn= a+(n-1)d  -- formula no.01.

Where

a = first term

d =   common difference.

n =  number of the  terms

tn =  nth term of the Arithmetic Progression (A.P)

Solution:

As given, -5 and 7.

Let Three arithmetic means are A,B and C which are inserted between -5 and 7.

The resulting  sequence will be Arithmetic Progression (A.P.) with  first term a and common difference d,

-5,A,B,C,7

First term a=-5

$5^{th}$ $term = 7$

Applying the formula no.01.

$(-5)+(5-1)d=7$

$-5+4d=7$

$4d=12$

$d=3$

First arithmetic mean,A $=a+d$

                                       $=-5+3= -2$

Second arithmetic mean,B $=a+2d$

                                             $=-5+2\times3= 1$

Third arithmetic mean,C$=a+3d$

                                         $=-5+3\times3= 4$

Thus,three arithmetic means between - 5 and 7 are -2, 1 and 4 .

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Answer 2

Answer:

-2, 1 and 4 are the required three arithmetic means between -5 and 7.

Step-by-step explanation:

Explanation:

Give two numbers -5 and 7.

• As we know, arithmetic means two numbers a and is $\frac{a + b}{2}$.

Let $A_1 , A_2 and A_3$ are the three arithmetic means between -5 and 7.

So,  -5,$A_1 , A_2 ,A_3, 7$  are in A.P.

• As we know, $A_1 , A_ 2, A_3 ...........A_n$ are n arithmetic between a and b where d = $\frac{b - a}{n + 1}$.

Step 1:

We have,   -5,$A_1 , A_2 ,A_3, 7$

a = -5 and b = 7 and n = 3

Now, first, we find out the value of d which stands for the common difference.

⇒ d = $\frac{b - a}{n + 1}$

⇒ d = $\frac{7 - -5}{3 + 1}$

⇒ d = $\frac{12}{4}$ = 3

Step 2:

As we have, $A _1 , A_2 and A_3$ are the required three arithmetic means.

⇒ $A_ 1 = a + d$

⇒ $A_ 1 = -5 + 3 = -2$

⇒ $A_2$ = a + 2d

⇒ $A_2$ = -5 + 2 (3) = -5 + 6 = 1

And $A_3$ = a + 3d

⇒ $A_ 3$ = -5 + 3 (3) = -5 + 9 = 4

Final answer:

Hence, -2, 1 and 4 are the required three arithmetic means between -5 and 7.

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