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Question
The sum of first 14 terms of an A.P. is 1050 and its 14th term is 140. Find the 20th term.
Solution
Let 'a' be the first term and 'd' be the common difference of the given A.P.
Given,
S14 = 1050
`\implies 14/2 [2a + (14 - 1)d] = 1050`
`\implies` 7[2a + 13d] = 1050
`\implies` 2a + 13d = 150
`\implies` a + 6.5d = 75 ...(i)
And t14 = 140
`\implies` a + 13d = 140 ...(ii)
Subtracting (i) from (ii), we get
6.5d = 65
⇒ d = 10
⇒ a + 13(10) = 140
⇒ a = 10
Thus, 20th term = t20
= 10 + 19d
= 10 + 19(10)
= 200
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