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  4. Let S be the sum of the first n terms of the arithmetic sequence 8, 12, 16, .....……., and T be the sum of first n terms arithmetic sequence 17, 19, 21, ….......….. . If S - T = 0, then the value of n is equal to

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Q. Let S be the sum of the first n terms of the arithmetic sequence 8, 12, 16, .....……., and T be the sum of first n terms arithmetic sequence 17, 19, 21, ….......….. . If $S - T = 0$, then the value of n is equal to

Sequences and Series

Solution:

$ S =\frac{ n }{2}[16+4( n -1)] ; T =\frac{ n }{2}[34+2( n -1)] $
$\therefore S - T =0 \Rightarrow 16+4 n -4=34+2 n -2 \Rightarrow 4 n +12=32+2 n \Rightarrow 2 n =20 \Rightarrow n =10$