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In the sequence S, the difference between any two consecutive terms is equal. If the sum of the fourth term and the fifth term of the sequence is equal to the seventh term of the sequence, what is the value of the second term of the sequence?
  • a)
    -4
  • b)
    0
  • c)
    4
  • d)
    8
  • e)
    Can't be determined
Correct answer is option 'B'. Can you explain this answer?
Verified Answer
In the sequence S, the difference between any two consecutive terms is...
Given
  • In a sequence S, difference between any two terms is equal
    • S is an arithmetic sequence
    • Let the first term of the sequence be a and the common difference be d
  • 4th   term + 5th  term = 7th  term
    • 4th  term = a + (4-1)*d = a+ 3d
    • 5th  term = a + (5-1)*d = a +4d
    • 7th term = a + (7-1)d = a + 6d
To Find: a + d = ?
Approach
  1. To find the value of a + d, we need to either find the values of a and d or a + d
  2. We are given a relation
    1. (a + 3d) + (a + 4d) = a + 6d
    2. As we are given only one equation between a and d, we will be unable to find the values of both a and b. So, we will try to see if we can find the value of a + d
 
Working Out
  1. (a + 3d) + (a+4d) = a+ 6d
    1. 2a + 7d = a + 6d
    2. a + d = 0
Hence, the value of the 2nd term of the sequence = a + d = 0
Answer: B
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