Question

Find five arithmetic means between 1 and 19

Answer 1

here 19-1=18 ,and 18/6 =3 so count the numbers by 3 .
1 ,4,7,10,13 ,16 ,19

Answer 2

Answer:

Required five arithmetic means between 1 and 19 are 4,7,10,13 and 16.

Step-by-step explanation:

Here given two numbers are 1 and 19.

We want to find five arithmetic means between 1 and 19

Let required 5 arithmetic means be $a_1,a_2,a_3,a_4,a_5$

We know,

nth term in AP series $= a + (n - 1) \times d$

Where a is the first term and d is common difference.

We know 7 th term of this series is 19 and first term is 1.

So,

$19 = 1 + (7 - 1) \times d \\ 19 = 1 + 6d \\ 6d = 19 - 1 \\ 6d = 18 \\ d = \frac{18}{6} \\ d = 3$

Therefore common difference of each term of this series is 3.

So,

2nd term $= (1 + 3) = 4$

3rd term $= (4 + 3) = 7$

4th term $= (7 + 3) = 10$

5th term $= (10 + 3) = 13$

6th term $= (13 + 3) = 16$

Hence, required five arithmetic means between 1 and 19 are 4,7,10,13 and 16.

Know more about Arithmetic progression:

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