Question

Solve.....................

Answer 1

3 + 6 + 9 + .............90 = ?
The above series is in the form of an arithmetic progression.
Here
last term (l) = 90
first term (a) = 3
common difference(d) =  3
number of terms (n) = ?

l = a + (n - 1)d
90 = 3 + (n - 1)3
90 = 3 + 3n - 3
3n = 90
n = 30.

The number of terms = 30.

We have to find the sum of the series.
Sum = n/2 (a + l)
         = 30/2 (3 + 90)
         = 15 * 93
         = 1395

The answer of your question is 1395.

Hope this helps you.  

Answer 2

Hii friend,

AP= 3,6,9,.......90

Here,

First term (a) = 3

Common difference (d) = 3

Tn = 90

a+(n-1) × d = 90

3 + (n-1) × 3 = 90

3 + 3n -3 = 90

3n = 90

n = 90/3

n = 30

Sum of nth term = Sn = N/2× [2a+(n-1) × d]

S30 = 30/2 × [ 2 × 3 + (30-1) × 3]

=> 30/2× (6 + 87)

=> 30/2× 93

=> 15 × 93

=> 1395 .

Hence,

3 + 6 + 9 + ...... + 90 = 1395

HOPE IT WILL HELP YOU..... :-)