Question

In an arithmetic sequence, T_(13)=27 and T_(7)=3T_(2). Find expressions in terms of n for T_(13),T_(7) and T_(2) and hence find the values of a and d. Write down the first six terms of the sequence.

Answer 1

The question involves finding the formula for the nth term of an arithmetic sequence and using it to determine the first term and common difference. It also includes finding the first six terms of the sequence.

Step-by-step explanation:

To find expressions for T_(13), T_(7), and T_(2) in an arithmetic sequence, we first define the nth term of an arithmetic sequence as T_n = a + (n-1)d, where 'a' is the first term and 'd' is the common difference between the terms. Given that T_(13) = 27 and T_(7) = 3T_(2), we can set up two equations:

• 
  
• T_(13) = a + (13 - 1)d = a + 12d = 27
• 
  
• T_(7) = a + (7 - 1)d = a + 6d
• 
  
• T_(2) = a + (2 - 1)d = a + d
• 
  
• T_(7) = 3T_(2) → a + 6d = 3(a + d)

Solving these equations simultaneously, we obtain the values for 'a' and 'd'.

Using these values, we can determine the first six terms of the sequence by starting with the first term 'a' and repeatedly adding the common difference 'd'.