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Find the (i) nth term and (ii) 12th term...

Find the (i) nth term and (ii) 12th term of the AP 14, 9, 4, -1, -6, …

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The given AP is 14, 9, 4, -1, -6, ….
Its first term = 14 and common difference = (9-14) = -5.
`therefore ` a = 14 and d = -5
(i) The nth term of the AP is given by
`T_(n) = a + (n -1)d`
`= 14 + (n-1) xx (-5) = (19-5n) [because a = 14 "and" d = -5]`
`therefore nth term = (19 -5n)`
(ii) 12th term of the given AP is
`T_(12) = a + ( 12- 1) d =(a + 11d)`
`= 14 xx 11 xx (-5) = -41 " " [because a = 14 "and" d = -5]`
`therefore ` 12th term = -41.
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