Find the sum to n terms of the sequence, 8, 88, 888, 8888…

Asked by Pragya Singh | 1 year ago |  108

##### Solution :-

Given sequence: 8, 88, 888, 8888…

This sequence is not a G.P.

But, it can be changed to G.P. by writing the terms as

Sn = 8 + 88 + 888 + 8888 + …………….. to n terms

$$\dfrac{8}{9}[9+99+999+9999$$

$$+....to\;n\;terms]$$

$$\dfrac{8}{9}[(10-1)+(10^2-1)+(10^3-1)$$

$$+(10^4-1)+.......to\;n\;terms]$$

$$\dfrac{8}{9}[10+10^2+....to\;n\;terms$$

$$-(1+1+1+..n\;tems)]$$

$$\dfrac{8}{9}[\dfrac{10(10^n-1)}{10-1}-n]$$

$$\dfrac{8}{9}[\dfrac{10(10^n-1)}{9}-n]$$

$$\dfrac{80}{81}(10^n-1)-\dfrac{8}{9}n$$

Answered by Abhisek | 1 year ago

### Related Questions

#### Construct a quadratic in x such that A.M. of its roots is A and G.M. is G.

Construct a quadratic in x such that A.M. of its roots is A and G.M. is G.

#### Find the two numbers whose A.M. is 25 and GM is 20.

Find the two numbers whose A.M. is 25 and GM is 20.

#### If a is the G.M. of 2 and 1/4 find a.

If a is the G.M. of 2 and $$\dfrac{1}{4}$$ find a.

#### Find the geometric means of the following pairs of numbers

Find the geometric means of the following pairs of numbers:

(i) 2 and 8

(ii) a3b and ab3

(iii) –8 and –2

#### Insert 5 geometric means between 32/9 and 81/2.

Insert 5 geometric means between $$\dfrac{32}{9}$$ and $$\dfrac{81}{2}$$.