Find the ` n^(th)` term of the series
` 2 + 5 + 10 + 17 + 26 + …`

Explanation

Let `S_(n) = 2 +5 +10+…+a_(n) ` (i)
Again , `underline( S_(n) = 2 +5 +…+ a_(n-1) +a_(n))` …(ii)
On subtracting , ` 0 = 2 + [3 +5 +7+…+(a_(n) -a_(n-1))] -a_(n)`
` rArr a_(n) = 2 = ((n-1))/(2) [ 2xx 3 + (n-1-1)xx2]`
` = 2 + (n-1)/(2) (6 +2n -4)`
` = 2 + (n-1) (n+1)`
` 2 + n^(2) -1 = n^(2) +1`
`therefore a_(n) = n^(2) +1`.