untitled

0DWK,;;)RUPD

Hence, in this case Sn aaa upto n.
an.
Activity : A employed a man from the first April for taking his son to school and
taking back home for a month. His wages were fixed to be – one paisa in first day,
twice of the first day in second day i.e. two paisa, twice of the second day in the
third day i.e. four paisa. If the wages were paid in this way, how much would he
get after one month including holidays of the week?

Example 9. What is the sum of the series 21  24  48  678?

Solution : The first term of the series is a 21 , common ratio 2 1.
12

24

r!

? the series is a geometric series.
Let the nth term of the series 768

We know, nth term =arn^1
? arn^1 768
or, 12 u 2 n^1 768
or, 64
12

2 n^1 768

or, 2 n^1 26
or, n 1 6
? n 7.

Therefore, the sum of the series ,
( 1 )

( 1 )





r

arn whenr! 1

12 ( 128 1 ) 12 127 1524.

2 1

12 ( 27 1 )

u  u





Example 10. ind the sum of first eight terms of the series F    
8

1

4

1

2

1

1

Solution : The 1st term of the series is a 1 , common ratio 1
2

1

1

2

1

r 

? It is a geomeric series.
Here the number of terms n 8.
We know, sum of nterms of a geometric series

,

1

( 1 )

r

S a rn

n 

 when r^1.

Hence, sum of eight terms of the series is

2

1

256

1 1

2

1 1

2

1 1 18

8





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128

1127

128

255

256

2256 ^1

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