Question

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

Answer 1

Sum of 100 terms = 25150

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

Answer 2

25150

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 = (n)/(2) * (2a + (n - 1) * d)`

If we plug in our values, we have:

`S = (100)/(2) * (2 * 4 + (100 - 1) * 5) = 50 * (8 + 99 * 5)`

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