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For an A.P the sum of first 30 terms is -1155,the common difference is -3and the thirtieth term is -82. What is the first term?
- a)10
- b)8
- c)5
- d)12
Correct answer is option 'C'. Can you explain this answer?
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Verified Answer
For an A.P the sum of first 30 terms is -1155,the common difference is...
l = a + (n - 1)d
Where l = -82,a = ?,d = -3,n = 30
-82 = a + 29 (- 3)
a = 5
Where l = -82,a = ?,d = -3,n = 30
-82 = a + 29 (- 3)
a = 5
Most Upvoted Answer
For an A.P the sum of first 30 terms is -1155,the common difference is...
Given: sum of first 30 terms = -1155, common difference = -3, thirtieth term = -82
To find: first term
Formula to find the sum of first n terms of an AP:
S_n = n/2[2a + (n-1)d]
where S_n is the sum of first n terms, a is the first term, d is the common difference.
Using the given values, we can form the equation:
-1155 = 30/2[2a + (30-1)(-3)]
-1155 = 15[2a - 87]
-1155 = 30a - 1305
30a = 150
a = 5
Therefore, the first term of the AP is 5. Hence, option (c) is the correct answer.
To find: first term
Formula to find the sum of first n terms of an AP:
S_n = n/2[2a + (n-1)d]
where S_n is the sum of first n terms, a is the first term, d is the common difference.
Using the given values, we can form the equation:
-1155 = 30/2[2a + (30-1)(-3)]
-1155 = 15[2a - 87]
-1155 = 30a - 1305
30a = 150
a = 5
Therefore, the first term of the AP is 5. Hence, option (c) is the correct answer.
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For an A.P the sum of first 30 terms is -1155,the common difference is...
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For an A.P the sum of first 30 terms is -1155,the common difference is -3and the thirtieth term is -82. What is the first term?a)10b)8c)5d)12Correct answer is option 'C'. Can you explain this answer?
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