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प्रश्न
The sum of first n terms of an AP is 3n2 + 4n. Find the 25th term of this AP ?
उत्तर
The sum of first n terms (Sn) is given as `S_n=3n^2+4n`.
So, first term (a1) =`S_n=3(1)^2+4(1)=7`
`S_2=a_1+a_2=3(2)^2+4(1)=7`
a2 = 20 − a1 = 20 − 7 = 13
So, common difference (d) = a2− a1 = 13 − 7 = 6
∴nth term is given by, an = a + (n − 1) d
Thus, 25th term = a25 = 7 + (25 − 1) × 6 = 7 + 24 × 6 = 7 + 144 = 151
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