Question

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

Answer 1

Answer:

25150

Step-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:

$S = \frac{n}{2} * (2a + (n - 1) * d)$

If we plug in our values, we have:

$S = \frac{100}{2} * (2 * 4 + (100 - 1) * 5) = 50 * (8 + 99 * 5)$

S = 50 * (8 + 495) = 50 * 503 = 25150

Answer 2

Answer:

Sum of 100 terms = 25150

Step-by-step explanation:

Formula:-

Sum of n terms of an AP

Sₙ = n/2[2a + (n - 1)d]

Where n - number of terms

a - first term and d - common difference

To find the sum of 100 terms

here, n = 100, a = 4 and d = 5

S₁₀₀ =  n/2[2a + (n - 1)d]

       = 100/2[2*4 + (100 - 1)5]

       = 50[8 + 99*5]

       = 25150