What is the sum of the first (5) terms of the arithmetic progression (3,13,23,33,\ldots)?

Correct answer: (115)

In an arithmetic progression, each term is found by adding the common difference to the previous term. The given progression starts at 3 and increases by 10, so its first five terms are 3, 13, 23, 33, and 43. To find their sum, add them directly: \(3+13+23+33+43=115\). Thus the correct choice is option C.

The same result follows from the arithmetic-series formula \(S_n=\frac{n}{2}(a+l)\), where n is the number of terms, a is the first term, and l is the last term. Here n=5, a=3, and l=43, so \(S_5=\frac{5}{2}(3+43)=\frac{5}{2}\times46=115\). The value 105 would omit some increase, while 110 and 125 do not equal the required sum.