A man purchased LCD TV for Rs. 32, 500. He paid Rs. 200 initially and increasing the payment by Rs. 150 every month. How many months did he take to make the complete payment?
The mount paid as down payment is 200Rs.
Amount paid in 1st instalment = 200 + 150 = 350Rs
Amount paid in 2nd instalment = 350 + 150 = 500Rs and so on.
The amount paid every month increase every month and forms finite AP. Which is : 200, 350, 500 ……..
Total amount paid is Sn = 32, 500Rs
we know that, Sn = 
× (2a + (n – 1)d)
⇒ 32, 500 = 
× (2(200) + (n – 1)(150))
⇒ 32, 500 = 
× (400 + 150n – 150)
⇒ 32, 500 = 
× (250 + 150n)
⇒ 32, 500 =n × (125 + 75n)
⇒ 75n2 + 125n – 32500 = 0
⇒ 25n2 + 5n – 1300 = 0
⇒ (3n + 65)(n – 20)=0
⇒ n = 
or n = 20
As n cannot be negative, so we have n = 20.
Thus we can say that there are 20 terms in the AP.
Among these terms first payment is the down payment, so man took 20 – 1 = 19 months to complete the payment.
∴ man took 19 months to complete the payment.
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