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If for an A.P. Sn=n2+7n what is its third term?
- a)21
- b)20
- c)15
- d)12
Correct answer is option 'D'. Can you explain this answer?
Verified Answer
If for an A.P. Sn=n2+7n what is its third term?a)21b)20c)15d)12Correct...
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If for an A.P. Sn=n2+7n what is its third term?a)21b)20c)15d)12Correct...
¶¶¶ we have Sn = n^2 + 7n
and to find out the 3rd term we must have first term i.e, (a) and a common difference i.e, ( d)
so let's use the above situation ¶¶¶
put n = 1
S1 = (1)^2 + 7×1
S1 = 8
we know that S1 = a1 = 8 ( first term)
now put n = 2 ¶¶¶
S2 = (2)^2 + 7×2
S2 = 18
we also know that
a2 = S2 - S1
a2 = 18 - 8
a2 = 10
now for common difference :- ¶¶¶
d= a2- a1
d = 10 - 8
d= 2
now we have a = 8 and d = 2 so let's find out the 3rd term i.e, a3= a+2d
= 8 +2 × 2
= 8 + 4
a3 = 12
so the third term is 12... .. ¶¶¶¶¶
and to find out the 3rd term we must have first term i.e, (a) and a common difference i.e, ( d)
so let's use the above situation ¶¶¶
put n = 1
S1 = (1)^2 + 7×1
S1 = 8
we know that S1 = a1 = 8 ( first term)
now put n = 2 ¶¶¶
S2 = (2)^2 + 7×2
S2 = 18
we also know that
a2 = S2 - S1
a2 = 18 - 8
a2 = 10
now for common difference :- ¶¶¶
d= a2- a1
d = 10 - 8
d= 2
now we have a = 8 and d = 2 so let's find out the 3rd term i.e, a3= a+2d
= 8 +2 × 2
= 8 + 4
a3 = 12
so the third term is 12... .. ¶¶¶¶¶
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Community Answer
If for an A.P. Sn=n2+7n what is its third term?a)21b)20c)15d)12Correct...
Given:
First term (a) = 1
Last term (l) = 11
Sum of terms = 36
To find: Number of terms (n)
Formula:
The sum of n terms of an arithmetic progression is given as:
S = n/2 [2a + (n-1)d]
where,
a = first term
d = common difference
l = last term
n = number of terms
Approach:
1. Using the given values, we can find the common difference (d) of the arithmetic progression.
2. Then, we can substitute the values of a, d, and l in the formula for the sum of n terms and simplify the equation to get the value of n.
Calculation:
Common difference (d) = l - a
= 11 - 1
= 10
Substituting the values in the formula for sum of n terms:
36 = n/2 [2(1) + (n-1)(10)]
36 = n/2 [2 + 10n - 10]
36 = n/2 [10n - 8]
72 = n(5n - 4)
5n² - 4n - 72 = 0
(n - 6)(5n + 12) = 0
n = 6 or -12/5
Since the number of terms cannot be negative, the answer is n = 6.
Therefore, the number of terms in the arithmetic progression is 6.
Answer: b) 6
First term (a) = 1
Last term (l) = 11
Sum of terms = 36
To find: Number of terms (n)
Formula:
The sum of n terms of an arithmetic progression is given as:
S = n/2 [2a + (n-1)d]
where,
a = first term
d = common difference
l = last term
n = number of terms
Approach:
1. Using the given values, we can find the common difference (d) of the arithmetic progression.
2. Then, we can substitute the values of a, d, and l in the formula for the sum of n terms and simplify the equation to get the value of n.
Calculation:
Common difference (d) = l - a
= 11 - 1
= 10
Substituting the values in the formula for sum of n terms:
36 = n/2 [2(1) + (n-1)(10)]
36 = n/2 [2 + 10n - 10]
36 = n/2 [10n - 8]
72 = n(5n - 4)
5n² - 4n - 72 = 0
(n - 6)(5n + 12) = 0
n = 6 or -12/5
Since the number of terms cannot be negative, the answer is n = 6.
Therefore, the number of terms in the arithmetic progression is 6.
Answer: b) 6
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If for an A.P. Sn=n2+7n what is its third term?a)21b)20c)15d)12Correct 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 for an A.P. Sn=n2+7n what is its third term?a)21b)20c)15d)12Correct 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 for an A.P. Sn=n2+7n what is its third term?a)21b)20c)15d)12Correct answer is option 'D'. Can you explain this answer?.
If for an A.P. Sn=n2+7n what is its third term?a)21b)20c)15d)12Correct 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 for an A.P. Sn=n2+7n what is its third term?a)21b)20c)15d)12Correct 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 for an A.P. Sn=n2+7n what is its third term?a)21b)20c)15d)12Correct answer is option 'D'. Can you explain this answer?.
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