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If the sum of n terms of an AP is 3n2+5n then which of its terms is 164?
- a)27th
- b)29th
- c)28th
- d)26th
Correct answer is option 'A'. Can you explain this answer?
Most Upvoted Answer
If the sum of n terms of an AP is 3n2+5n then which of its terms is 16...
Sn=3n^2+5n
S1=a1=3(1)^2+5(1)=8
S2=3(2)^2+5(2)=22
S2=22=a1+a2
a2=22-8=14
d=a2-a1=14-8=6
n^th term value is 164,then what is n?
n^th term=a+(n-1)d
164=8+(n-1)6
164-8 / 6=n-1
156/6=n-1
26+1=n
n=27
So 27^th term is 164.
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Community Answer
If the sum of n terms of an AP is 3n2+5n then which of its terms is 16...
Given: Sum of n terms of an AP = 3n^2+5n
To find: Which term is 164?
Solution:
Let's assume that the first term of the AP is 'a' and the common difference is 'd'.
The sum of n terms of an AP can be expressed as:
S_n = n/2 [2a + (n-1)d]
We are given that S_n = 3n^2+5n
So, we can write:
3n^2+5n = n/2 [2a + (n-1)d]
Simplifying this equation, we get:
6n^2 + 10n = n(2a + (n-1)d)
Dividing both sides by n, we get:
2a + (n-1)d = 6n + 10
Now, we know that the nth term of an AP can be expressed as:
a_n = a + (n-1)d
We need to find the value of n for which a_n = 164.
Substituting a_n = 164 and simplifying, we get:
n^2 + 4n - 41 = 0
Solving this quadratic equation, we get:
n = 5 or n = -9
Since n has to be a positive integer, we can ignore n = -9.
Therefore, the required term is the 27th term (when n = 5).
Hence, the correct answer is option 'A'.
To find: Which term is 164?
Solution:
Let's assume that the first term of the AP is 'a' and the common difference is 'd'.
The sum of n terms of an AP can be expressed as:
S_n = n/2 [2a + (n-1)d]
We are given that S_n = 3n^2+5n
So, we can write:
3n^2+5n = n/2 [2a + (n-1)d]
Simplifying this equation, we get:
6n^2 + 10n = n(2a + (n-1)d)
Dividing both sides by n, we get:
2a + (n-1)d = 6n + 10
Now, we know that the nth term of an AP can be expressed as:
a_n = a + (n-1)d
We need to find the value of n for which a_n = 164.
Substituting a_n = 164 and simplifying, we get:
n^2 + 4n - 41 = 0
Solving this quadratic equation, we get:
n = 5 or n = -9
Since n has to be a positive integer, we can ignore n = -9.
Therefore, the required term is the 27th term (when n = 5).
Hence, the correct answer is option 'A'.
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If the sum of n terms of an AP is 3n2+5n then which of its terms is 164?a)27thb)29thc)28thd)26thCorrect answer is option 'A'. 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 the sum of n terms of an AP is 3n2+5n then which of its terms is 164?a)27thb)29thc)28thd)26thCorrect answer is option 'A'. 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 the sum of n terms of an AP is 3n2+5n then which of its terms is 164?a)27thb)29thc)28thd)26thCorrect answer is option 'A'. Can you explain this answer?.
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