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What is the nth term of A.P 1, 3, 5, 7, _____?
  1. n
  2. n²
  3. 2n - 1
  4. None of these
Explanation
The given sequence is an arithmetic progression (AP) of odd numbers:
1,3,5,7,...1 comma 3 comma 5 comma 7 comma point point point
.
The formula for the $n$th term (
ana sub n
) of an AP is
an=a+(n−1)da sub n equals a plus open paren n minus 1 close paren d
.
  1. Identify the first term (
    aa
    )    :
    a=1a equals 1
    .
  2. Identify the common difference (
    dd
    )    : The difference between consecutive terms is constant.
    3−1=23 minus 1 equals 2
    ,
    5−3=25 minus 3 equals 2
    , etc. So,
    d=2d equals 2
    .
  3. Substitute the values into the formula:
    an=1+(n−1)2a sub n equals 1 plus open paren n minus 1 close paren 2

  4. Simplify the expression:

    a_n=1+2n-2

    a_n=2n-1





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