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What is the sum of the first 15 terms of an A.P whose 11 th and 7 th terms are 5.25 and 3.25 respectively
- a)56.25
- b)60
- c)52.5
- d)none of these
Correct answer is option 'A'. Can you explain this answer?
Verified Answer
What is the sum of the first 15 terms of an A.P whose 11 th and 7 th ...
a +10d = 5.25, a+6d = 3.25, 4d = 2, d = 1/4
a +5 = 5.25, a = 0.25 = 1/4, s 15 = 15/2 ( 2 * 1/4 + 14 * 1/4 )
= 15/2 (1/2 +14/2 ) = 15/2 *15/2 =225/ 4 = 56.25
Most Upvoted Answer
What is the sum of the first 15 terms of an A.P whose 11 th and 7 th ...
To find the sum of the first 15 terms of an arithmetic progression (A.P), we need to know the common difference (d) between the terms. Let's use the given information to find the common difference.
Given:
11th term (a11) = 5.25
7th term (a7) = 3.25
We can use the formula for the nth term of an A.P to find the common difference:
a11 = a1 + (11 - 1) * d
5.25 = a1 + 10d
a7 = a1 + (7 - 1) * d
3.25 = a1 + 6d
Now, we have two equations with two variables (a1 and d). We can solve these equations simultaneously to find the values of a1 and d.
Subtracting the second equation from the first equation, we get:
5.25 - 3.25 = a1 + 10d - a1 - 6d
2 = 4d
d = 0.5
Substituting the value of d in the second equation, we can find a1:
3.25 = a1 + 6 * 0.5
3.25 = a1 + 3
a1 = 0.25
Therefore, the first term (a1) of the A.P is 0.25 and the common difference (d) is 0.5.
Now, we can find the sum of the first 15 terms of the A.P using the formula:
Sn = (n/2) * (2a1 + (n-1) * d)
Substituting the values, we get:
S15 = (15/2) * (2 * 0.25 + (15 - 1) * 0.5)
S15 = 7.5 * (0.5 + 14 * 0.5)
S15 = 7.5 * (0.5 + 7)
S15 = 7.5 * 7.5
S15 = 56.25
Therefore, the sum of the first 15 terms of the A.P is 56.25. Hence, the correct answer is option A.
Given:
11th term (a11) = 5.25
7th term (a7) = 3.25
We can use the formula for the nth term of an A.P to find the common difference:
a11 = a1 + (11 - 1) * d
5.25 = a1 + 10d
a7 = a1 + (7 - 1) * d
3.25 = a1 + 6d
Now, we have two equations with two variables (a1 and d). We can solve these equations simultaneously to find the values of a1 and d.
Subtracting the second equation from the first equation, we get:
5.25 - 3.25 = a1 + 10d - a1 - 6d
2 = 4d
d = 0.5
Substituting the value of d in the second equation, we can find a1:
3.25 = a1 + 6 * 0.5
3.25 = a1 + 3
a1 = 0.25
Therefore, the first term (a1) of the A.P is 0.25 and the common difference (d) is 0.5.
Now, we can find the sum of the first 15 terms of the A.P using the formula:
Sn = (n/2) * (2a1 + (n-1) * d)
Substituting the values, we get:
S15 = (15/2) * (2 * 0.25 + (15 - 1) * 0.5)
S15 = 7.5 * (0.5 + 14 * 0.5)
S15 = 7.5 * (0.5 + 7)
S15 = 7.5 * 7.5
S15 = 56.25
Therefore, the sum of the first 15 terms of the A.P is 56.25. Hence, the correct answer is option A.
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