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Consider the following question and deci...

Consider the following question and decide which of the statements is sufficient to answer the question.
Question:
Find the seventh letter in the series (Arithmetic progression)
Statements:
I. if the first letter in the series is 2.
II. if the common difference in A.P is 3.

A

Only statement I is sufficient

B

Both statements I and II are sufficient

C

Either statement I or II is sufficient

D

Only statement II is sufficient

Text Solution

AI Generated Solution

The correct Answer is:
To solve the question of finding the seventh letter in an arithmetic progression (A.P.), we need to analyze the provided statements step by step. ### Step-by-Step Solution: 1. **Understanding the A.P.**: An arithmetic progression is defined by its first term and the common difference. The nth term of an A.P. can be calculated using the formula: \[ a_n = a + (n - 1) \cdot d \] where \( a \) is the first term, \( d \) is the common difference, and \( n \) is the term number. 2. **Analyzing Statement I**: - Statement I states that the first letter in the series is 2. This gives us the value of \( a \): \[ a = 2 \] - However, without knowing the common difference \( d \), we cannot determine the terms of the A.P. Therefore, Statement I alone is **not sufficient**. 3. **Analyzing Statement II**: - Statement II states that the common difference in the A.P. is 3. This gives us the value of \( d \): \[ d = 3 \] - However, without knowing the first term \( a \), we cannot determine the terms of the A.P. Therefore, Statement II alone is **not sufficient**. 4. **Combining Both Statements**: - Now, if we combine both statements, we have: - First term \( a = 2 \) - Common difference \( d = 3 \) - We can now use the A.P. formula to find the 7th term: \[ a_7 = a + (7 - 1) \cdot d \] \[ a_7 = 2 + 6 \cdot 3 \] \[ a_7 = 2 + 18 = 20 \] - Thus, the seventh letter in the series is **20**. ### Conclusion: To find the seventh letter in the series, we need both statements. Therefore, the answer is that both statements together are sufficient to answer the question.
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