Question

Find the sum to 'n' terms of the sequence 6,66,666,6666..​

Answer 1

Answer:

6+66+666……n

To solve this type question 1st we need to find which type series is created means Arithmetic progression or Geometric progression.

=6(1+11+111+…………..n)

=6*(9/9)(1+11+111+…………..n)

=(6/9)(9+99+999………….n)

now,

=(6/9)((10–1)+(100–1)+(1000–1)………..n)

=(6/9)[(10+100+1000…….n)-(1+1+1……..n)]

=(6/9)[(10+10^2+10^3………n) - (1+1+1……..n)]

now this is in Geometric progression.

r = 10

a=10

now put in the formula

Sn= a1(r^n-1)/r-1

where r=! 1

Sn = (6/9)[(10(10^n-1)/(10–1))- n]

Step-by-step explanation: