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In an A.P., if common difference is 2, Sum of n terms is 49, 7th term is 13 tthen then n = _________.
- a)0
- b)5
- c)7
- d)13
Correct answer is option 'C'. Can you explain this answer?
Most Upvoted Answer
In an A.P., if common difference is 2, Sum of n terms is 49, 7thterm i...
Given, common difference (d) = 2, Sum of n terms (Sₙ) = 49, 7th term (a₇) = 13
We know that the sum of n terms of an A.P. is given by the formula:
Sₙ = n/2[2a + (n-1)d]
where a is the first term of the A.P.
We can use this formula to find the first term (a) of the A.P.:
49 = n/2[2a + (n-1)2]
98 = n[2a + (n-1)2]
98 = 2an + 2n² - 2n
n² + (a-1)n - 49 = 0
Now, we can use the given information about the 7th term to form another equation:
a₇ = a + 6d
13 = a + 6(2)
13 = a + 12
a = 1
Substituting a = 1 in the equation we got earlier:
n² + (1-1)n - 49 = 0
n² - 49 = 0
n = ±7
Since n cannot be negative, n = 7.
Therefore, the number of terms in the A.P. is 7 (option C is correct).
We know that the sum of n terms of an A.P. is given by the formula:
Sₙ = n/2[2a + (n-1)d]
where a is the first term of the A.P.
We can use this formula to find the first term (a) of the A.P.:
49 = n/2[2a + (n-1)2]
98 = n[2a + (n-1)2]
98 = 2an + 2n² - 2n
n² + (a-1)n - 49 = 0
Now, we can use the given information about the 7th term to form another equation:
a₇ = a + 6d
13 = a + 6(2)
13 = a + 12
a = 1
Substituting a = 1 in the equation we got earlier:
n² + (1-1)n - 49 = 0
n² - 49 = 0
n = ±7
Since n cannot be negative, n = 7.
Therefore, the number of terms in the A.P. is 7 (option C is correct).
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Community Answer
In an A.P., if common difference is 2, Sum of n terms is 49, 7thterm i...
Tn = a + (n - 1) d
T7 = a + (7 - 1) 2
13 = a + (6) 2
13 = a + 12
13 - 12 = a
1 = a
Sn = n/2 [2a + (n - 1) d]
49 = n/2 [2×1 + (n - 1) 2]
49 = n/2 [2 + 2n - 2]
49 = n/2 × 2n
49 = n²
7 = n
Option C
T7 = a + (7 - 1) 2
13 = a + (6) 2
13 = a + 12
13 - 12 = a
1 = a
Sn = n/2 [2a + (n - 1) d]
49 = n/2 [2×1 + (n - 1) 2]
49 = n/2 [2 + 2n - 2]
49 = n/2 × 2n
49 = n²
7 = n
Option C
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In an A.P., if common difference is 2, Sum of n terms is 49, 7thterm is 13 tthen then n = _________.a)0b)5c)7d)13Correct answer is option 'C'. Can you explain this answer?
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