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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Step 1: $a + a_8 = 32 \Rightarrow 2a + 7d = 32$ ... (i)
Step 2: $a 	imes a_8 = 60 \Rightarrow a(a + 7d) = 60$ ... (ii)
Step 3: Solving (i) and (ii), we get
$a = 2$ or $a = 30$
and $d = 4$ or $d = -4$
Step 4: First term and common difference of A.P. are $2$ and $4$ or $30$ and $-4$ respectively.
Step 5: Now, for $a = 2$ and $d = 4$:
$S_{20} = 10(4 + 76) = 800$
and for $a = 30$ and $d = -4$:
$S_{20} = 10(60 - 76) = -160$

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