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If the sum of three consecutive terms of an increasing A.P. is 51 and the product of the first and third of these terms is 273, then the third term is
- a)13
- b)9
- c)21
- d)17
Correct answer is option 'C'. Can you explain this answer?
Verified Answer
If the sum of three consecutive terms of an increasing A.P. is 51 and ...
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
⇒ 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
⇒ a2 –d2 = 273
⇒ 172 –d 2 = 273
⇒ 289 –d 2 = 273
⇒ d 2 = 289 –273
⇒ d 2 = 16
⇒ d = 4
⇒ a2 –d2 = 273
⇒ 172 –d 2 = 273
⇒ 289 –d 2 = 273
⇒ d 2 = 289 –273
⇒ d 2 = 16
⇒ d = 4
Hence the 3rd terms ( a+d ) is 21
This question is part of UPSC exam. View all GMAT courses
Most Upvoted Answer
If the sum of three consecutive terms of an increasing A.P. is 51 and ...
Given:
Sum of three consecutive terms = 51
Product of first and third terms = 273
Let's assume the first term of the arithmetic progression (A.P.) is 'a' and the common difference is 'd'.
Sum of three consecutive terms:
The second term will be 'a + d' and the third term will be 'a + 2d'. Adding these three terms gives us:
a + (a + d) + (a + 2d) = 51
Simplifying the equation:
3a + 3d = 51
Dividing by 3:
a + d = 17 --- (Equation 1)
Product of first and third terms:
The product of the first and third terms is 'a * (a + 2d)'. Given that this product is equal to 273, we can write the equation:
a * (a + 2d) = 273
Expanding the equation:
a^2 + 2ad = 273 --- (Equation 2)
Solving the equations:
From Equation 1, we have:
a + d = 17
Rearranging the terms:
a = 17 - d
Substituting this value of 'a' in Equation 2:
(17 - d)^2 + 2d(17 - d) = 273
Expanding and simplifying the equation:
289 - 34d + d^2 + 34d - 2d^2 = 273
d^2 - 2d^2 + 34d - 34d + 289 - 273 = 0
-d^2 + 16 = 0
Simplifying the equation:
d^2 = 16
Taking the square root of both sides:
d = ±4
Since the common difference of an A.P. cannot be negative, we take d = 4.
Substituting this value of 'd' in Equation 1:
a + 4 = 17
a = 13
Therefore, the third term of the A.P. is 'a + 2d':
13 + 2(4) = 13 + 8 = 21
Hence, the correct answer is option C) 21.
Sum of three consecutive terms = 51
Product of first and third terms = 273
Let's assume the first term of the arithmetic progression (A.P.) is 'a' and the common difference is 'd'.
Sum of three consecutive terms:
The second term will be 'a + d' and the third term will be 'a + 2d'. Adding these three terms gives us:
a + (a + d) + (a + 2d) = 51
Simplifying the equation:
3a + 3d = 51
Dividing by 3:
a + d = 17 --- (Equation 1)
Product of first and third terms:
The product of the first and third terms is 'a * (a + 2d)'. Given that this product is equal to 273, we can write the equation:
a * (a + 2d) = 273
Expanding the equation:
a^2 + 2ad = 273 --- (Equation 2)
Solving the equations:
From Equation 1, we have:
a + d = 17
Rearranging the terms:
a = 17 - d
Substituting this value of 'a' in Equation 2:
(17 - d)^2 + 2d(17 - d) = 273
Expanding and simplifying the equation:
289 - 34d + d^2 + 34d - 2d^2 = 273
d^2 - 2d^2 + 34d - 34d + 289 - 273 = 0
-d^2 + 16 = 0
Simplifying the equation:
d^2 = 16
Taking the square root of both sides:
d = ±4
Since the common difference of an A.P. cannot be negative, we take d = 4.
Substituting this value of 'd' in Equation 1:
a + 4 = 17
a = 13
Therefore, the third term of the A.P. is 'a + 2d':
13 + 2(4) = 13 + 8 = 21
Hence, the correct answer is option C) 21.
Community Answer
If the sum of three consecutive terms of an increasing A.P. is 51 and ...
Let's say these 3 terms are x-y, x, and x+y
(x-y)+x+(x+y) = 51
3x=51
so, x= 17
(x-y)*(x+y) = 273
x^2 - y^2= 273
(17^2) - y^2 = 273
289-y^2= 273
y^2 = 16
y = 2
4
so the numbers are
(17-4), 17, and (17+4)
13, 17, 21
(x-y)+x+(x+y) = 51
3x=51
so, x= 17
(x-y)*(x+y) = 273
x^2 - y^2= 273
(17^2) - y^2 = 273
289-y^2= 273
y^2 = 16
y = 2
4
so the numbers are
(17-4), 17, and (17+4)
13, 17, 21
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If the sum of three consecutive terms of an increasing A.P. is 51 and the product of the first and third of these terms is 273, then the third term isa)13b)9c)21d)17Correct answer is option 'C'. Can you explain this answer?
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If the sum of three consecutive terms of an increasing A.P. is 51 and the product of the first and third of these terms is 273, then the third term isa)13b)9c)21d)17Correct answer is option 'C'. Can you explain this answer? for GMAT 2025 is part of GMAT preparation. The Question and answers have been prepared according to the GMAT exam syllabus. Information about If the sum of three consecutive terms of an increasing A.P. is 51 and the product of the first and third of these terms is 273, then the third term isa)13b)9c)21d)17Correct answer is option 'C'. Can you explain this answer? covers all topics & solutions for GMAT 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for If the sum of three consecutive terms of an increasing A.P. is 51 and the product of the first and third of these terms is 273, then the third term isa)13b)9c)21d)17Correct answer is option 'C'. Can you explain this answer?.
If the sum of three consecutive terms of an increasing A.P. is 51 and the product of the first and third of these terms is 273, then the third term isa)13b)9c)21d)17Correct answer is option 'C'. Can you explain this answer? for GMAT 2025 is part of GMAT preparation. The Question and answers have been prepared according to the GMAT exam syllabus. Information about If the sum of three consecutive terms of an increasing A.P. is 51 and the product of the first and third of these terms is 273, then the third term isa)13b)9c)21d)17Correct answer is option 'C'. Can you explain this answer? covers all topics & solutions for GMAT 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for If the sum of three consecutive terms of an increasing A.P. is 51 and the product of the first and third of these terms is 273, then the third term isa)13b)9c)21d)17Correct answer is option 'C'. Can you explain this answer?.
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