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The sum of first and eighth terms of an A.P. is $32$ and their product is $60$. Find the first term and common difference of the A.P. Hence, also find the sum of its first $20$ terms.
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Sol. $a + a_8 = 32 \Rightarrow 2a + 7d = 32$ ----- (i)
$a \times a_8 = 60 \Rightarrow a(a + 7d) = 60$ ----- (ii)
Solving (i) & (ii), we get
$a=2$ or $a = 30$
and $d = 4$ or $d = -4$
First term and common difference of A.P. are $2$ and $4$ or $30$ and $-4$ respectively.
$a \times a_8 = 60 \Rightarrow a(a + 7d) = 60$ ----- (ii)
Solving (i) & (ii), we get
$a=2$ or $a = 30$
and $d = 4$ or $d = -4$
First term and common difference of A.P. are $2$ and $4$ or $30$ and $-4$ respectively.