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

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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.

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