Question

Insert three arithmetic means between 3 and 15

Answer 1

Answer:

3,6,9,12,15

Step-by-step explanation:

3+15/2=9

3+9/2=6

9+15/2=12

Answer 2

Step-by-step explanation:

Given: 3 and 15

To find: Insert two arithmetic means between given numbers.

Solution:

If two n arithmetic means are inserted between two numbers a and b, then new common difference:

$\bf d = \frac{b - a}{n + 1}$

Step 1: Find new difference.

Two AM are inserted, so n=2

$d = \frac{15 - 3}{2 + 1}$

or

$d = \frac{12}{3}$

or

$\bf d = 4$

Step 2: Insert AM's

We know that general term of AP is given by

$\bf a_n = a + (n - 1)d$

here

$a = 3$

$d = 4$

$a_2 = 3 + (2 - 1)4$

$a_2 = 7$

By the same way

$a_3 = 3 + 2 \times 4$

or

$a_3 = 11$

Final answer:

Two AM's are 7 and 11.

New AP is $3, \: 7, \: 11, \: 15$

Hope it helps you.

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