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Find the sum of first 20 terms of an A.P. whose $n^{th}$ term is given by $a_n = 5 + 2n$. Can 52 be a term of this A.P.?
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$a_n = 5 + 2n \Rightarrow a = 7, d = 2$ (1 mark)
$S_{20} = \frac{20}{2} [14 + 19 \times 2] = 520$ (1 mark)
$52 = 7 + (n - 1) \times 2 \Rightarrow n = \frac{47}{2}$, which is not a natural number. ($\frac{1}{2}$ mark)
Therefore, 52 cannot be a term of this A.P. ($\frac{1}{2}$ mark)
$S_{20} = \frac{20}{2} [14 + 19 \times 2] = 520$ (1 mark)
$52 = 7 + (n - 1) \times 2 \Rightarrow n = \frac{47}{2}$, which is not a natural number. ($\frac{1}{2}$ mark)
Therefore, 52 cannot be a term of this A.P. ($\frac{1}{2}$ mark)