Question

what is the arithematic progression of 333​

Answer 1

Answer:

Let the sum of the given sequence be S_{n}S

n

So, S_{n}S

n

= 3 + 33 + 333 + .... + n

S_{n}S

n

= 3( 1 + 11 + 111 + .... upto\:n\:terms )

Divide and multiply by 9.

S_{n}=\dfrac{3}{9}\bigg( 9 + 99 + 999 + ...\mathsf{upto\:n\:terms}\:\bigg)S

n

=

9

3

(9+99+999+...uptonterms)

S_{n} = \dfrac{1}{3}\bigg[ ( 10 - 1 ) + ( 100 - 1 ) + ( 100 - 1 ) + .... + \mathsf{upto\:n\:terms}\bigg]S

n

=

3

1

[(10−1)+(100−1)+(100−1)+....+uptonterms]