Mathematics
Grade10
Easy

Question

The explicit formula for the sequence 360, 180, 90, 45 … is __________

  1. a subscript n end subscript equals open parentheses fraction numerator 1 over denominator 2 end fraction close parentheses to the power of n minus 1 end exponent    
  2. a subscript n end subscript equals 360 cross times open parentheses fraction numerator 1 over denominator 2 end fraction close parentheses to the power of n minus 1 end exponent    
  3. a subscript n end subscript equals 45 cross times open parentheses 2 close parentheses to the power of 3 end exponent    
  4. a subscript n end subscript equals fraction numerator 1 over denominator 2 end fraction cross times open parentheses 360 close parentheses to the power of n minus 1 end exponent    

Hint:

In this question, we have to find the explicit formula for the sequence 360, 180, 90, 45 … As the explicit formula for GP is a subscript n end subscript equals a subscript 1 end subscript cross times open parentheses r close parentheses to the power of n minus 1 end exponent, where a is the first term, r is the constant ratio of the geometric sequence and n is the number of terms. So, by putting the available information, we can find the required explicit formula.

The correct answer is: a subscript n end subscript equals 360 cross times open parentheses fraction numerator 1 over denominator 2 end fraction close parentheses to the power of n minus 1 end exponent


    The explicit formula for a geometric sequence is a subscript n end subscript equals a subscript 1 end subscript cross times open parentheses r close parentheses to the power of n minus 1 end exponent
    First term, a = 360
    The constant ratio of the geometric sequence, r = fraction numerator 180 over denominator 360 end fraction equals fraction numerator 1 over denominator 2 end fraction
    So, the explicit formula for the given sequence is a subscript n end subscript equals 360 cross times open parentheses fraction numerator 1 over denominator 2 end fraction close parentheses to the power of n minus 1 end exponent

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