Class 10 Exam > Class 10 Questions > If Ss= 32, S4 = 28~~What is ts=?a)36b)24c)8d)...
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If Ss = 32, S4 = 28 ~~ What is ts =?
- a)36
- b)24
- c)8
- d)4
Correct answer is option 'D'. Can you explain this answer?
Most Upvoted Answer
If Ss= 32, S4 = 28~~What is ts=?a)36b)24c)8d)4Correct answer is option...
Given, Ss= 32 and S4 = 28
To find, ts=?
We know that the sum of an arithmetic progression (AP) is given by the formula:
Sn = n/2[2a + (n-1)d]
where Sn is the sum of first n terms, a is the first term, d is the common difference and n is the number of terms.
Let's find the common difference (d) of this AP.
S4 = 4/2[2a + (4-1)d] = 2[2a + 3d] = 4a + 6d
Given that S4 = 28, we have:
4a + 6d = 28
Similarly, for Ss, we have:
Ss = s/2[2a + (s-1)d] = s/2[a + a + (s-1)d] = (s/2)[2a + (s-1)d]
Given that Ss = 32, we have:
(s/2)[2a + (s-1)d] = 32
Dividing both sides by 4, we get:
(s/8)[2a + (s-1)d] = 8
Now, we can substitute the value of a + 3d from the equation 4a + 6d = 28 into the above equation, to get:
(s/8)[2(a + 3d) + (s-4)d] = 8
Simplifying this, we get:
s^2 - 16s + 64 = 0
This is a quadratic equation that can be factored as:
(s-8)(s-8) = 0
Therefore, the only possible value of s is 8.
Hence, the answer is option D, ts = 4.
To find, ts=?
We know that the sum of an arithmetic progression (AP) is given by the formula:
Sn = n/2[2a + (n-1)d]
where Sn is the sum of first n terms, a is the first term, d is the common difference and n is the number of terms.
Let's find the common difference (d) of this AP.
S4 = 4/2[2a + (4-1)d] = 2[2a + 3d] = 4a + 6d
Given that S4 = 28, we have:
4a + 6d = 28
Similarly, for Ss, we have:
Ss = s/2[2a + (s-1)d] = s/2[a + a + (s-1)d] = (s/2)[2a + (s-1)d]
Given that Ss = 32, we have:
(s/2)[2a + (s-1)d] = 32
Dividing both sides by 4, we get:
(s/8)[2a + (s-1)d] = 8
Now, we can substitute the value of a + 3d from the equation 4a + 6d = 28 into the above equation, to get:
(s/8)[2(a + 3d) + (s-4)d] = 8
Simplifying this, we get:
s^2 - 16s + 64 = 0
This is a quadratic equation that can be factored as:
(s-8)(s-8) = 0
Therefore, the only possible value of s is 8.
Hence, the answer is option D, ts = 4.
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If Ss= 32, S4 = 28~~What is ts=?a)36b)24c)8d)4Correct answer is option...
See use formula of sum of nth term u will get two equations then slove it..
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If Ss= 32, S4 = 28~~What is ts=?a)36b)24c)8d)4Correct answer is option 'D'. Can you explain this answer? for Class 10 2025 is part of Class 10 preparation. The Question and answers have been prepared according to the Class 10 exam syllabus. Information about If Ss= 32, S4 = 28~~What is ts=?a)36b)24c)8d)4Correct answer is option 'D'. Can you explain this answer? covers all topics & solutions for Class 10 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for If Ss= 32, S4 = 28~~What is ts=?a)36b)24c)8d)4Correct answer is option 'D'. Can you explain this answer?.
If Ss= 32, S4 = 28~~What is ts=?a)36b)24c)8d)4Correct answer is option 'D'. Can you explain this answer? for Class 10 2025 is part of Class 10 preparation. The Question and answers have been prepared according to the Class 10 exam syllabus. Information about If Ss= 32, S4 = 28~~What is ts=?a)36b)24c)8d)4Correct answer is option 'D'. Can you explain this answer? covers all topics & solutions for Class 10 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for If Ss= 32, S4 = 28~~What is ts=?a)36b)24c)8d)4Correct answer is option 'D'. Can you explain this answer?.
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