Question

find the sum of of the sequence 7,77,777,7777,..... to n terms​

Answer 1

Ok it is not in Arithmetic Progression so we cannot find till nth terms but if the value of n get fixed then with the help of calculators we can !

( ╹▽╹ )

Answer 2

Given and To find:

- Find the sum of of the sequence 7,77,777,7777,..... to terms.

According to the given question:

- This is not a G.P, But we can relate it to G.P by writing in terms.

→ $\sf{s_{n} = 7 + 77 + 777 + 7777 + ....n \: terms}$

→ $\sf{\frac{7}{9}(9 + 99 + 999 + 9999)....n \: terms}$

→ $\sf{\frac{7}{9} ((10 - 1) + (10 {}^{2} - 1)(10 {}^{3} - 1) + \\: (10 {}^{4} - 1) + ....n \: terms)}$

→ $\sf{\frac{7}{9} ((10 + 10 {}^{2} + 10 {}^{3} + ....n \: terms ) - (1 + 1 + 1....n \: terms))}$

→ $\sf{\frac{7}{9} ( \frac{10(10 {n}^{2} - 1) }{10 - 1} - n)}$

→ ${\sf{\boxed{\frac{7}{9} ( \frac{10(10 {}^{n} - 1)}{9} - n)}}}$