Saved Bookmarks
| 1. |
Tommy Hunk's plane crashed on an island as he was travelling to his championship in Honduras. After recovering from the crash landing, he was delighted to find that his 40-litre bucket for protein potion survived the crash as well. A realist, he decides that he will use his resources carefully. He drinks one litre of the protein potion on day one of his stays. He adds water to the container to make up the volume. The next day, he consumes 2 litres of the solution. He again adds water to the container to make up the volume. The day after he repeats the same, except this time he drinks 3 litres of the solution. As luck would have it, he was rescued the day he finished the contents of the container. How much water did he drink during his stay on the island? |
|
Answer» ong>Answer: Answer: First term = 1 Common difference = 6 Given STATEMENTS about the terms of an AP: 9th term = 7 × 2nd Term 9th term = 7 × 2nd Term12th term = 5 × 3rd term + 2 We have to find the following: First term, a Common difference, d The STANDARD form of an AP is: a , a + d, a + 2d , a + 3d, ... , a + (n - 1)d Where, a = first term of AP d = common difference of AP So, According to the formula, aₙ = a + (n - 1)d We have 9th term and 2nd term as a + 8d and a + d respectively. So According to the STATEMENT given, ⇒ 9th term = 7 × 2nd term ⇒ a + 8d = 7 (a + d) ⇒ a + 8d = 7a + 7d ⇒ 7a - a + 7d - 8d = 0 ⇒ 6a - d = 0 ...(i) Similarly, According to the second statement, we have ⇒ 12th term = ( 5 × 3rd term ) + 2 ⇒ a + 11d = { 5(a + 2d) } + 2 ⇒ a + 11d = 5A + 10d + 2 ⇒ 5a - a + 10d - 11d = -2 ⇒ 4a - d = -2 ...(ii) Subtract eq.(ii) from eq.(i), we get ⇒ 6a - d - (4a - d) = 0 - (-2) ⇒ 6a - d - 4a + d = 2 ⇒ 6a - 4a = 2 ⇒ 2a = 2 ⇒ a = 1 We found the first term to be 1, Hence substitute the value of a in eq.(i), we get ⇒ 6a - d = 0 ⇒ 6(1) - d = 0 ⇒ 6 - d = 0 ⇒ d = 6 |
|