Puzzle Patel was out looking for a new apartment to rent. The landlord asks him if he has any pets.
Patel: "Three cats"
Landlord: "How old are they?"
Patel: "The product of their ages is 72."
Landlord: "What kind of answer is that!? I need more information."
Patel: "Sorry, that must have been unclear. The sum of the ages of my pets is the same as your house number."
Landlord: "Still not enough information, As we have only 20 houses in this society."
Patel: "My oldest cat is called Gypsy and sum of letters and her age is related as perfect square"
Landlord: "Okay, cool. Now that I know their ages, you can have the house."
What is the sum of the ages of Puzzle Patel's pets
Answers
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
Answer:
It has to be 17 or 19
Step-by-step explanation:
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