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If the sum of three consecutive terms of an AP is 51 and the product of two extremes is 273. Find the third numbers.?
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If the sum of three consecutive terms of an AP is 51 and the product o...
Let 3 consecutive terms A.P is a –d, a , a + d. and the sum is 51
so, (a –d) + a + (a + d) = 51
> 3a –d + d = 51
> 3a = 51
> a = 17
The product of first and third terms is 273
So it stand for ( a –d) (a + d) = 273
>a 2 –d 2 = 273
> 172 –d 2 = 273
> 289 –d 2 = 273
> d 2 = 289 –273
> d 2 = 16
> d = (plus and minus) 4
so now put plus and minus eventually to get the third term.
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If the sum of three consecutive terms of an AP is 51 and the product o...
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If the sum of three consecutive terms of an AP is 51 and the product o...
Let's solve the problem step by step:
Step 1: Identify the given information
- The sum of three consecutive terms of an arithmetic progression (AP) is 51.
- The product of the first and third terms is 273.
Step 2: Define the terms of the AP
- Let's assume the three consecutive terms of the AP as 'a-d', 'a', and 'a+d', where 'a' is the second term and 'd' is the common difference.
Step 3: Express the given information in terms of the defined terms
- The sum of the three terms is 51, so we can write the equation as:
(a-d) + a + (a+d) = 51
- The product of the first and third terms is 273, so we can write the equation as:
(a-d) * (a+d) = 273
Step 4: Solve the equations
Let's solve the equations simultaneously:
From the first equation, we can simplify it to:
3a = 51
a = 17
Substituting the value of 'a' into the second equation:
(17-d) * (17+d) = 273
289 - d^2 = 273
d^2 = 289 - 273
d^2 = 16
d = ±4
Step 5: Find the third term
Since we have two possible values for 'd', let's calculate the corresponding third terms for each value:
- For d = 4:
Third term = a + d = 17 + 4 = 21
- For d = -4:
Third term = a + d = 17 - 4 = 13
Step 6: Final answer
Therefore, the possible third terms of the AP are 21 and 13.
Step 1: Identify the given information
- The sum of three consecutive terms of an arithmetic progression (AP) is 51.
- The product of the first and third terms is 273.
Step 2: Define the terms of the AP
- Let's assume the three consecutive terms of the AP as 'a-d', 'a', and 'a+d', where 'a' is the second term and 'd' is the common difference.
Step 3: Express the given information in terms of the defined terms
- The sum of the three terms is 51, so we can write the equation as:
(a-d) + a + (a+d) = 51
- The product of the first and third terms is 273, so we can write the equation as:
(a-d) * (a+d) = 273
Step 4: Solve the equations
Let's solve the equations simultaneously:
From the first equation, we can simplify it to:
3a = 51
a = 17
Substituting the value of 'a' into the second equation:
(17-d) * (17+d) = 273
289 - d^2 = 273
d^2 = 289 - 273
d^2 = 16
d = ±4
Step 5: Find the third term
Since we have two possible values for 'd', let's calculate the corresponding third terms for each value:
- For d = 4:
Third term = a + d = 17 + 4 = 21
- For d = -4:
Third term = a + d = 17 - 4 = 13
Step 6: Final answer
Therefore, the possible third terms of the AP are 21 and 13.
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If the sum of three consecutive terms of an AP is 51 and the product of two extremes is 273. Find the third numbers.?
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If the sum of three consecutive terms of an AP is 51 and the product of two extremes is 273. Find the third numbers.? for CA Foundation 2024 is part of CA Foundation preparation. The Question and answers have been prepared according to the CA Foundation exam syllabus. Information about If the sum of three consecutive terms of an AP is 51 and the product of two extremes is 273. Find the third numbers.? covers all topics & solutions for CA Foundation 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for If the sum of three consecutive terms of an AP is 51 and the product of two extremes is 273. Find the third numbers.?.
If the sum of three consecutive terms of an AP is 51 and the product of two extremes is 273. Find the third numbers.? for CA Foundation 2024 is part of CA Foundation preparation. The Question and answers have been prepared according to the CA Foundation exam syllabus. Information about If the sum of three consecutive terms of an AP is 51 and the product of two extremes is 273. Find the third numbers.? covers all topics & solutions for CA Foundation 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for If the sum of three consecutive terms of an AP is 51 and the product of two extremes is 273. Find the third numbers.?.
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