Write first four terms of the sequence given by ` a_(n)= 1/6 ( 2n-3)` and obtain the corresponding series.

Explanation

We have , ` a_(n) = 1/6 ( 2n-3)`
Putting n= 1,2,3,4,…, successively in ( i) we get
` a_(1) = 1/6( 2xx 1-3) = (-1)/6, a_(2) = 1/6 ( 2xx 2-3) = 1/6 `
` a_(3) = 1/6 ( 2xx 3-3) = 3/6 = 1/2 , a_(4) = 1/6 ( 2 xx 4-3) = 5/6`
Hence, the required sequence is `( -1)/6, 1/6, 1/2 ,5/6 ,.....,`
The corresponding series is `- 1/6 + 1/6 + 1/2 + 5/6+ ` ....