Find the first three terms of the following sequences and write down the corresponding series :
(i) `a_(n) = 5n + 2`
(ii) `a_(1) = 1, a_(n) = a_(n - 1) + 5` for ` n ge 2 `

Explanation

(i) Given , `a_(n) = 5n + 2 `
Putting n = 1 , 2, 3 we get ,
`a_(1) = 5 xx 1 + 2 = 7`
` a_(2) = 5xx 2 + 2 = 12 `
` a_(3) = 5 xx 3 + 2 = 17`
Hence , the first three term of the sequence are 7, 12 and 17
The corresponding series is ` 7 + 12 + 17 + ...`
(ii) ` a_(1) = 1 . a_(n) = a_(n-1) + 5` for ` nge 2 `
Putting n = 2 , 3 we get
` a_(2) = a_(1) + 5 = 1 + 5 = 6`
` a_(3) = a_(2) + 5 = 6 + 5 = 11`
Hence , the first three terms of the sequence are 1, 6 and 11
The corresponding series is ` 1 + 6 + 11 + ...`