Answer :
Final answer:
The given series is a geometric series with the first term 'a' as 103 and the common ratio 'r' as 103, matching option (a) a = 103, r = 103, from the choices given.
Explanation:
The series in question is 103, 1032, 1033, 1034, ⋯ which may seem confusing at first, but we can understand it better by examining a similar concept from scientific notation. In scientific notation, when powers of 10 are multiplied together, their exponents are added together. For instance, if we had 10² × 10³, it would equal 10²+3, which is 10µ.
Now, back to the series: The terms of the series appear to be the base number 103 raised to the power of 1, then 2, then 3, and so forth. To recognize this series as a geometric series, we need to identify the first term 'a' and the common ratio 'r'.
The first term 'a' is the base of our series, which is 103. The common ratio 'r' is the factor by which each term in the series is multiplied to get the next term. Since each 'increase' in power is by a factor of 103, then the common ratio is also 103. Thus, the correct representation of the series as a geometric series is: a = 103, r = 103, which corresponds to option (a).
