Question

Find the 25th term of an arithmetic sequence if the first term is 7 and the common difference is 3

Answer 1

79

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The general formula for the nth term of an arithmetic sequence is given by:

• 
  `\[ a_n = a_1 + (n - 1)d \]`

where:

• 
  `\( a_1 \)` is the first term,
• 
  `\( n \)` is the term number,
• 
  `\( d \)` is the common difference.
  

In this case, you are given:

• 
  `\( a_1 = 7 \)` (the first term is 7),
• 
  `\( d = 3 \)` (the common difference is 3),
• 
  `\( n = 25 \)` (we're looking for the 25th term).
  

We'll plug these values into the general formula to find the 25th term:

• 
  `\[ a_(25) = 7 + (25 - 1) \cdot 3 \]`
• 
  `\[ a_(25) = 7 + 24 \cdot 3 \]`
• 
  `\[ a_(25) = 7 + 72 \]`
• 
  `\[ a_(25) = 79 \]`

So, the 25th term of the arithmetic sequence is 79.