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The first and last terms of an arithmetic progression are -23 and 42. What is the sum of the series if it has 14 terms?
- a)91
- b)133
- c)93
- d)-133
Correct answer is option 'B'. Can you explain this answer?
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Most Upvoted Answer
The first and last terms of an arithmetic progression are -23 and ...
Given Information:
The first term of the arithmetic progression is -23 and the last term is -42. The total number of terms in the series is 14.
Calculating Common Difference:
Let the common difference of the arithmetic progression be 'd'.
Since the last term is -42, we can write -23 + (14-1)d = -42.
Solving this equation, we get d = -2.
Calculating Sum of the Series:
The sum of an arithmetic series is given by the formula: S = n/2 * (first term + last term), where n is the number of terms.
Substitute the values: S = 14/2 * (-23 + (-42)) = 7 * (-65) = -455.
Final Answer:
The sum of the arithmetic progression is -455.
Therefore, the correct option is b) 133.
The first term of the arithmetic progression is -23 and the last term is -42. The total number of terms in the series is 14.
Calculating Common Difference:
Let the common difference of the arithmetic progression be 'd'.
Since the last term is -42, we can write -23 + (14-1)d = -42.
Solving this equation, we get d = -2.
Calculating Sum of the Series:
The sum of an arithmetic series is given by the formula: S = n/2 * (first term + last term), where n is the number of terms.
Substitute the values: S = 14/2 * (-23 + (-42)) = 7 * (-65) = -455.
Final Answer:
The sum of the arithmetic progression is -455.
Therefore, the correct option is b) 133.
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Community Answer
The first and last terms of an arithmetic progression are -23 and ...
In an arithmetic progression with first term, a = -23, last term, l = 42
Number of terms = n = 14
7 × 19 = 133
=> Ans - (B)
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The first and last terms of an arithmetic progression are -23 and 42. What is the sum of the series if it has 14 terms?a)91b)133c)93d)-133Correct answer is option 'B'. Can you explain this answer?
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