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# Find the sum to n terms of the given sequence is 8, 88, 888, ....

**Solution:**

The given sequence is 8, 88, 888, .... n terms .

S_{n} = 8 + 88 + 888 + .... n terms

= 8 [9 + 99 + 999 + .... terms]

= 8/9 [(10 - 1) + (100 - 1) + (1000 - 1) + .... n terms]

= 8/9 [(10 + 10^{2} + 10^{3} + .... n terms) - (1 + 1 + 1 + .... n terms)]

= 8/9 [10 (10^{n} - 1)/(10 - 1) - n]

= 8/9 [10 (10^{n} - 1)/9 - n]

= 80/81 (10^{n} - 1) - 8/9 n

NCERT Solutions Class 11 Maths Chapter 9 Exercise 9.3 Question 18

## Find the sum to n terms of the given sequence is 8, 88, 888,...

**Summary:**

The sum of the first n terms of the sequence 8, 88, 888, ... is 80/81 (10^{n} - 1) - 8/9 n

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