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Billy gave money to a charity over a 20 year period, from Year 1 to Year 20 inclusive. He gave RM150 in Year 1, RM160 in Year 2, RM170 in year 3, and so on. Kevin also gave money to the charity over the same 20 years period. He gave RMA im Year 1 and the amount of money he gave each year increased, forming an arithmetic sequence with common difference RM30. The total amount of money that Kevin gave over 20 years period was twice the total amount of money that Billy gave. calculate the value of A. ​

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The value of A is RM 205.

Since Billy gave money to a charity over a 20 year period, from Year 1 to Year 20 inclusive, and he gave RM150 in Year 1, RM160 in Year 2, RM170 in year 3, and so on, and Kevin also gave money to the charity over the same 20 years period, but he gave RMA im Year 1 and the amount of money he gave each year increased, forming an arithmetic sequence with common difference RM30, and the total amount of money that Kevin gave over 20 years period was twice the total amount of money that Billy gave, to calculate the value of A the following calculation must be performed:

  • Billy = (150 x 20) + 10 + 20 + 30 + 40 + 50 + 60 + 70 + 80 + 90 + 100 + 110 + 120 + 130 + 140 + 150 + 160 + 170 + 180 + 190
  • Billy = (150 x 20) + 1900
  • Billy = 3000 + 1900
  • Billy = 4900
  • Kevin = (9800 - (30 + 60 + 90 + 120 + 150 + 180 + 210 + 240 + 270 + 300 + 330 + 360 + 390 + 420 + 450 + 480 + 510 + 540 + 570)) / 20
  • Kevin = (9800 - 5700) / 20
  • Kevin = 4100/20
  • Kevin = 205

Therefore, the value of A is RM 205.

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