Find the indicated sum. 6+9+12+15+⋯+183

Question

Find the indicated sum.   6+9+12+15+⋯+183

anonymous · Answer

this is an arithmetic progression with the 1st term A = 6, common difference D = 3, and the last term L = 183.

We need to find the no. of terms N

now L = A + (N-1)D

183 = 6 + (N-1)3

177 = (N-1)3

59 = N-1 OR N = 60

Now sum of an A.P. = N/2 ( A+L)

A = FIRST TERM OF SERIES; L = LAST TERM OF SERIES

=> 60/2(6+183)

=> 30 X 189 = 5670 is the answer. :)

anonymous · Answer

What is first term and common difference here??

anonymous · Answer

6 and 3

anonymous · Answer

Yep..
And you have last term an given, so :

$$a_n = a + (n -1)d \implies 183 = 6 + (n - 1) \cdot 3$$

Can you find n here??

anonymous · Answer

60

anonymous · Answer

Yep..

So you are one step away now from answer:

Use:

$$\large \color{green}{Sum = \frac{n}{2}(a + a_n)}$$

anonymous · Answer

i have the answer already

anonymous · Answer

Okay, then best of luck...