Find the (i) nth term and (ii) 16th term of the AP 3, 5, 7, 9, 11, …

Explanation

The given AP is 3, 5, 7, 9, 11, …
Its first term = 3 and common difference = (5-3) = 2.
`therefore` a= 3 and d = (5-3) = 2.
(i) Its nth term is given by
`T_(n) = a + (n-1)d`
` = 3 +(n-1) xx 2 = (2n +1) " " [because a = 3 "and" d = 2].`
`therefore "nth term" = (2n +1)`
(ii) 16th term of the given AP is
`T_(16) = a + (16 -1)d = (a + 15d)`
` = (3 + 15 xx 2) = 33 " " [because a= 3 "and" d= 2]`
`therefore ` 16th term = 33.`