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Mathematics

Grade10

Easy

Question

What is the 10^th term of the geometric sequence 10.5, 21, 42, 84…?

5376
1208
9221
4217

hint Hint:

The nth term of a geometric progression is, $a subscript n end subscript equals a subscript 1 end subscript cross times open parentheses r close parentheses to the power of n minus 1 end exponent$

The correct answer is: 5376

Using the explicit formula, $a subscript n end subscript equals a subscript 1 end subscript cross times open parentheses r close parentheses to the power of n minus 1 end exponent$
For the given sequence, the constant ratio is $fraction numerator 21 over denominator 10.5 end fraction equals 2$
So, $a subscript 10 end subscript equals 10.5 cross times open parentheses 2 close parentheses to the power of 9 end exponent$
$equals 10.5 cross times 512$
= 5376

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