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Four times the ninety first term of an arithmetic progression is equal to 5 times it's eighty first term. If the thirty first term of the progression is -630 , find its fifty term.?
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Four times the ninety first term of an arithmetic progression is equal...
Problem: Four times the ninety first term of an arithmetic progression is equal to 5 times it's eighty first term. If the thirty first term of the progression is -630 , find its fifty term.
Solution:
Let the first term of the arithmetic progression be 'a' and the common difference be 'd'.
Therefore, the ninety first term of the progression will be 'a + 90d' and the eighty first term will be 'a + 80d'.
Given, 4(a + 90d) = 5(a + 80d)
Simplifying the above expression, we get:
a = 50d
We know that the thirty first term of the progression is -630.
Therefore, substituting the values of 'a' and 'd', we get:
50d + 30d = -630
80d = -630
d = -7.875
Substituting the value of 'd' in the equation 'a = 50d', we get:
a = -393.75
Therefore, the arithmetic progression is: -393.75, -401.625, -409.5, ...
To find the fiftieth term, we use the formula:
T50 = a + 49d
Substituting the values of 'a' and 'd', we get:
T50 = -393.75 + 49(-7.875)
T50 = -393.75 - 386.625
T50 = -780.375
Therefore, the fiftieth term of the progression is -780.375.
Answer: The fiftieth term of the arithmetic progression is -780.375.
Solution:
Let the first term of the arithmetic progression be 'a' and the common difference be 'd'.
Therefore, the ninety first term of the progression will be 'a + 90d' and the eighty first term will be 'a + 80d'.
Given, 4(a + 90d) = 5(a + 80d)
Simplifying the above expression, we get:
a = 50d
We know that the thirty first term of the progression is -630.
Therefore, substituting the values of 'a' and 'd', we get:
50d + 30d = -630
80d = -630
d = -7.875
Substituting the value of 'd' in the equation 'a = 50d', we get:
a = -393.75
Therefore, the arithmetic progression is: -393.75, -401.625, -409.5, ...
To find the fiftieth term, we use the formula:
T50 = a + 49d
Substituting the values of 'a' and 'd', we get:
T50 = -393.75 + 49(-7.875)
T50 = -393.75 - 386.625
T50 = -780.375
Therefore, the fiftieth term of the progression is -780.375.
Answer: The fiftieth term of the arithmetic progression is -780.375.
Community Answer
Four times the ninety first term of an arithmetic progression is equal...
4(a+90d)=5(a+80d)
4a+360d=5a+400d
a=-40d...(1)
[a+30d=-630]...(given)....(2)
Putting value of (1) in equation (2);
-40d+30d=-630
-10d=-630
d=63
a=-40(63)
a=-2520
....50th term=>a+49d
-2520+49(63)
3087-2520
567...(Required Answer!)
4a+360d=5a+400d
a=-40d...(1)
[a+30d=-630]...(given)....(2)
Putting value of (1) in equation (2);
-40d+30d=-630
-10d=-630
d=63
a=-40(63)
a=-2520
....50th term=>a+49d
-2520+49(63)
3087-2520
567...(Required Answer!)
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Four times the ninety first term of an arithmetic progression is equal to 5 times it's eighty first term. If the thirty first term of the progression is -630 , find its fifty term.?
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Four times the ninety first term of an arithmetic progression is equal to 5 times it's eighty first term. If the thirty first term of the progression is -630 , find its fifty term.? for CAT 2024 is part of CAT preparation. The Question and answers have been prepared according to the CAT exam syllabus. Information about Four times the ninety first term of an arithmetic progression is equal to 5 times it's eighty first term. If the thirty first term of the progression is -630 , find its fifty term.? covers all topics & solutions for CAT 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Four times the ninety first term of an arithmetic progression is equal to 5 times it's eighty first term. If the thirty first term of the progression is -630 , find its fifty term.?.
Four times the ninety first term of an arithmetic progression is equal to 5 times it's eighty first term. If the thirty first term of the progression is -630 , find its fifty term.? for CAT 2024 is part of CAT preparation. The Question and answers have been prepared according to the CAT exam syllabus. Information about Four times the ninety first term of an arithmetic progression is equal to 5 times it's eighty first term. If the thirty first term of the progression is -630 , find its fifty term.? covers all topics & solutions for CAT 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Four times the ninety first term of an arithmetic progression is equal to 5 times it's eighty first term. If the thirty first term of the progression is -630 , find its fifty term.?.
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