Question

(b) Insert 4 arithmetic means between 2 and -16.

Answer 1

Solution:-

To Find

$\sf \to \: 4 \: \: arithmetic \: \: mean \: \: between \: 2 \: \: and \: \: - 16$

$\sf \to - 16, \underline{ \: \: \: \: \: \: \: },\underline{ \: \: \: \: \: \: \: },\underline{ \: \: \: \: \: \: \: },\underline{ \: \: \: \: \: \: \: },2$

Now we can write as

$\sf \to \: \: - 16 + d,- 16 + 2d,- 16 + 3d,- 16 + 4d,$

Formula

$\sf \to \: 2 = - 16 + (n - 1)d$

$\sf \to \: 2 + 16 = (4 - 1)d$

$\sf\to \: 18 = 3d$

$\sf \to \: d = \dfrac{18}{3} = 6$

So we get d = 6

Now put the value of d

$\sf \to \: \: - 16 + d,- 16 + 2d,- 16 + 3d,- 16 + 4d,$

$\sf \to \: \: - 16 + 6,- 16 + 2 \times 6,- 16 + 3 \times 6,- 16 + 4 \times 6,$

$\sf \to \: - 10, - 16 + 12, - 16 + 18 ,- 16 + 24$

$\sf \to \: - 10, -4, 2 ,8$

Answer

$\sf \to \: - 10, -4, 2 ,8$