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प्रश्न
The sum of first 14 terms of an A.P. is 1050 and its 14th term is 140. Find the 20th term.
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उत्तर
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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