Question

Find the nth term of the following sequence :
5 + 55 +555 + . . . . Tn
A.5(10n - 1)
B.5n(10n - 1)
C.(5/9)*(10n - 1)
D.(5/9)n *10n - 1)

Answer 1

Answer:

heya!!

here is your answer:

5 [ 1+11+111+...+N]

Multiplying and dividing by 9

(5/9) [ 9 +99+999+...+N]

(5/9) [ (10-1) + ( 10²-1) + ( 10³-1) +...+ N]

(5/9)[ 10 + 10² + 10³ + ...+N ] -[ 1+1+1+1+...+N]

{Now 10 10² 10³ ... N are in g.p

an = 10(10^N-1 ). }

(5/9) [ 10^N -1]

hope it helps!

Answer 2

Hi Mate!!!

The given series is neither in g.p nor in a.p so, let's make it one of the asked form.

=>. 5 [ 1 +11 +111 +...+ n]

Multiple and Divide by 9

=>. 5/9[ 9+99+999+...+n]

=>. 5/9[ (10 -1) + ( 10²-1) +( 10³-1 ) +...+ N]

=>. 5 /9 [ 10 + 10² +10³ +...+N ] - [ 1+1+1+1...N]

10 + 10² + 10³+...+ N are in g.p

=>. 5/9 [ 10^N -1]

Have a nice day