Question

the sum of n terms of 2 arithmetic series are in the ratio 2n-1:2n+1. whats the ratio of the 10th term?

Answer 1

#Sn=n/2 2a+(n-1)d use thus formula instead of Sn=n/2(a+Tn)

Answer 2

Answer:-

Sol. Let the two arithmetic series be a, a + d, a + 2d ..... and A, A + D, A + 2D, .... .

Given that, 2[2 ( 1) ] 2 1

2[2 ( 1) ] 2 1

n an d n

n An D n

+− + = +− −

⇒ 2 ( 1) 2 1

2 ( 1) 2 1

an d n

An D n

+− + = +− − ...(i)

Ratio of the 10th terms of these series = 10

10

9 2 18

9 2 18

t ad a d

T AD A D

+ + = = + +

\ Putting n = 19 in (i), we have 10

10

2 18 2 19 1

2 18 2 19 1

t a d

T AD

+ ×+ = = + ×−

=

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