Each question is followed by two statements, A and B. Answer each ques...
Let the first term and common difference of the given arithmetic series be a and d respectively.
Using statement A alone:
The first term of the series is 17.
a =17
We need to find the tenth term i.e. a + 9d.
Since we cannot find the value of d from the above information, we cannot find the value of the tenth term.
Thus, the question cannot be answered using statement A alone.
Using statement B alone:
The sum of the fourth term and the sixteenth term of the given series is 142.
a + 3d + a + 15d = 142
i.e. 2a+ 18d= 142
i.e. a + 9d = 71
Thus, the tenth term of the given series is 71.
Thus, the question can be answered using statement B alone.
Thus, the question can be answered using statement B alone but not by using statement A alone.
Hence, option 2.
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Each question is followed by two statements, A and B. Answer each ques...
Statement A: The first term of the arithmetic series is 17.
Statement B: The sum of the fourth term and the sixteenth term of the arithmetic series is 142.
To find the tenth term of the given arithmetic series, we need to determine the common difference of the series and then calculate the tenth term.
Analysis:
Let's analyze each statement and see if it alone is sufficient to answer the question.
Statement A: The first term of the arithmetic series is 17.
This statement gives us the value of the first term, but it doesn't provide any information about the common difference or the specific pattern of the series. Therefore, statement A alone is not sufficient to answer the question.
Statement B: The sum of the fourth term and the sixteenth term of the arithmetic series is 142.
This statement provides information about the sum of the fourth term and the sixteenth term, but it doesn't give us any information about the individual terms or the common difference. Therefore, statement B alone is not sufficient to answer the question.
Using both statements together:
To find the tenth term, we need information about the common difference of the series. If we combine the two statements, we can find the common difference and then calculate the tenth term.
Let's assume that the common difference of the arithmetic series is 'd'.
From statement A, we know that the first term is 17.
From statement B, we know that the sum of the fourth term and the sixteenth term is 142. Using the formula for the sum of an arithmetic series, we can write the equation as:
17 + (4-1)d + 17 + (16-1)d = 142
34 + 3d + 17 + 15d = 142
32d + 51 = 142
32d = 91
d = 91/32
Now, we have the value of the common difference 'd'. We can use this to find the tenth term by using either statement A or B.
Therefore, the question can be answered by using both statements together.
Conclusion:
The correct answer is option (4) - The question can be answered by using both the statements together but not by either of the statements alone.
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