What is the sum of the first 100 terms of the sequence 4,9,14,19, ...?

Answer:25150Step-by-step explanation:First, we have to see that this is an arithmetic sequence... since to get the next element we add 5 to it.  (a geometric sequence would be a multiplication, not an addition)So, we have a, the first term (a = 4), and we have the difference between each term (d = 5), and we want to find the SUM of the first 100 terms.To do this without spending hours writing them down, we can use this formula:[tex]S = \frac{n}{2} * (2a + (n - 1) * d)[/tex]If we plug in our values, we have:[tex]S = \frac{100}{2} * (2 * 4 + (100 - 1) * 5) = 50 * (8 + 99 * 5)[/tex]S = 50 * (8 + 495) = 50 * 503 = 25150