Find the first five terms of the following sequences and write down the corresponding series
(i) ` a_(n) = (1)/(5) (2n -3)`
(ii) `a_(1) =a_(2) = 1 , a_(n) = a_(n-1) + a_(n-2) , n gt 2 `

Explanation

Given ` a_(n) = (1)/(5) (2n-3)`
` therefore a_(1) = (1)/(5) (2 -3) = (-1)/(5)`
` a_(2) = (1)/(5) (4 -3) = (10/(5)` ,
` a_(3) = (1)/(5) (6-3) = (3)/(5)`
` a_(4) = (1)/(5) (8-3) = 1`
` a_(5) = (1)/(5) (10 -3) = (7)/(5)`
The corresponding series is : ` (-1)/(5) + (1)/(5) + (3)/(5) + 1+ (7)/(5) + ...`
(ii) Given , ` a_(1) = a_(2) = 1 , a_(n) = a_(n-1) + a_(n-2) . n gt 2 `
` therefore a_(3) = a_(2) + a_(1) = 1 + 1 = 2 `,
` a_(4) = a_(3) + a_(2) = 2 + 1 = 3 ` ,
` a_(5) = a_(4) + a_(3) = 3 + 2 = 5`
The corresponding series is : ` 1 + 1 + 2 + 3 + 5 + ...` .