Question

how many terms of the series 42,36,30.................amount 150

Answer 1

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• Here a=42 , d = 36-42 = -6
• Suppose S(n) = 150
• S(n) = n/2 × (2a + (n-1) d)
• 150 = n/2 × (84+(n-1) -6)
• 300=n( 84-6n+6)
• 300=n(90-6n)
• 50 = n(15-n)
• 50= 15n-n^2
• ${n}^{2} - 15n + 50 = 0$
• ${n}^{2} - 5n - 10n + 50 = 0$
• $n(n - 5) - 10(n - 5) = 0$
• $n = 10 \: \: or \: \: n = 5$
• Hope it helps!