Question

Find the sum 3+6+9+..............+60

Answer 1

Answer: 630

Step-by-step explanation: 3 + 6 + 9 ... 60

Take 3 common then 3(1 + 2 + 3... + 20)

the sum of 1 + 2 + 3... + 20 can be found by the formula of n(n + 1)/2  which is 20 x 21 /2 = 210

∴ 3 + 6 + 9 + ... + 60 = 3 x 210 = 630

Answer 2

The sum of 3+6+9+..............+60 is 630.

Given:

3+6+9+..............+60

To find:

The sum of the above.

Solution:

• We can solve this by using the formula for arithmetic progression.
• For that instead of considering it as the sum of the terms let's consider the given sum as an arithmetic progression(as there is a common difference between the two terms)
• First, we will find out the number of terms in the series and then the sum of the terms.

To find the number of terms in assumed arithmetic sequence:

We know that the nth term of an arithmetic progression is given by,

$t_{n} =a+(n-1)d$.

Now,

• $t_{n}$=60
• a=3
• d=6-3 =3

     $t_{n}$= 3 + (n-1)* 3

⇒60 = 3 + 3n-3

⇒3n=60

⇒n=20

The number of terms in the assumed arithmetic progression is 20.

To find the sum of the given terms:

Sum of the terms is arithmetic progression is given by,

$S_{n} = \frac{n}{2} [2a+(n-1)*d]$

$S_{n} =\frac{20}{2} [2(3)+(20-1)*3]$

    = 10 [6 + 19*3]

    = 10 [6 + 57]

    = 10(63)

    = 630

Hence, the sum of 3+6+9+..............+60 is 630.      

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