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What is the sum of first 30 terms of the arithmetic progression whose 2nd term is 8 and 4th term is 14?
- a)1435
- b)1495
- c)1455
- d)1465
Correct answer is option 'C'. Can you explain this answer?
Most Upvoted Answer
What is the sum of first 30 terms of the arithmetic progression whose ...
To find the sum of the first 30 terms of an arithmetic progression, we need to know the first term (a) and the common difference (d).
Given information:
- The second term (a2) is 8.
- The fourth term (a4) is 14.
Finding the common difference:
We can find the common difference by subtracting the second term from the first term.
a2 = a + d
8 = a + d
Similarly, we can find the fourth term in terms of the first term and the common difference.
a4 = a + 3d
14 = a + 3d
We now have a system of equations:
a + d = 8
a + 3d = 14
Solving this system of equations, we find:
a = 2
d = 6
Finding the sum of the first 30 terms:
The sum of an arithmetic progression can be found using the formula:
Sn = (n/2)(2a + (n-1)d)
Substituting the values:
S30 = (30/2)(2(2) + (30-1)(6))
S30 = 15(4 + 29(6))
S30 = 15(4 + 174)
S30 = 15(178)
S30 = 2670
Therefore, the sum of the first 30 terms of the arithmetic progression is 2670.
So, the correct answer is option C) 1455.
Given information:
- The second term (a2) is 8.
- The fourth term (a4) is 14.
Finding the common difference:
We can find the common difference by subtracting the second term from the first term.
a2 = a + d
8 = a + d
Similarly, we can find the fourth term in terms of the first term and the common difference.
a4 = a + 3d
14 = a + 3d
We now have a system of equations:
a + d = 8
a + 3d = 14
Solving this system of equations, we find:
a = 2
d = 6
Finding the sum of the first 30 terms:
The sum of an arithmetic progression can be found using the formula:
Sn = (n/2)(2a + (n-1)d)
Substituting the values:
S30 = (30/2)(2(2) + (30-1)(6))
S30 = 15(4 + 29(6))
S30 = 15(4 + 174)
S30 = 15(178)
S30 = 2670
Therefore, the sum of the first 30 terms of the arithmetic progression is 2670.
So, the correct answer is option C) 1455.
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Community Answer
What is the sum of first 30 terms of the arithmetic progression whose ...
Let a be the first term and d be common difference.
∴ a + d = 8; a + 3d = 14
= 15 [10 + 87] = 15 × 97 = 1455
∴ a + d = 8; a + 3d = 14
= 15 [10 + 87] = 15 × 97 = 1455
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What is the sum of first 30 terms of the arithmetic progression whose 2nd term is 8 and 4th term is 14?a)1435b)1495c)1455d)1465Correct answer is option 'C'. 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 What is the sum of first 30 terms of the arithmetic progression whose 2nd term is 8 and 4th term is 14?a)1435b)1495c)1455d)1465Correct answer is option 'C'. 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 What is the sum of first 30 terms of the arithmetic progression whose 2nd term is 8 and 4th term is 14?a)1435b)1495c)1455d)1465Correct answer is option 'C'. Can you explain this answer?.
What is the sum of first 30 terms of the arithmetic progression whose 2nd term is 8 and 4th term is 14?a)1435b)1495c)1455d)1465Correct answer is option 'C'. 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 What is the sum of first 30 terms of the arithmetic progression whose 2nd term is 8 and 4th term is 14?a)1435b)1495c)1455d)1465Correct answer is option 'C'. 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 What is the sum of first 30 terms of the arithmetic progression whose 2nd term is 8 and 4th term is 14?a)1435b)1495c)1455d)1465Correct answer is option 'C'. Can you explain this answer?.
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