Question

1 , 3 , 6 , 10 , 15

Answer 1

Answer:

1. a_n = a_(n-1) + n where a_1 is 1 or a_n = n(n+1)/2

2. 231

Step-by-step explanation:

Notice that from 1 to 3, you add 2; from 3 to 6, you add 3; from 6 to 10, you add 4, etc. The pattern here is add 2, add 3, add 4, add 5, etc.

1. Let the nth term be a_n. The recursive equation can be written as a_n = a_(n-1) + n where a_1 = 1 (Use this because they most likely teach you this in schools)

Here is it written in an arithmetic equation (most likely not taught in school):

We can write an arithmetic expression using the summation formula because it is basically the sum of the numbers from 1 to n, so a_n = n(n+1)/2

2. Using the recursive, we would need to constantly add until you get up to a_21, which would take a while. Using the arithmetic equation, we can simply get:

21(21+1)/2 = 21(11) = 231

I hope this helps! :)

Answer 2

As we can see that common difference is increasing to one more digit after every term

so it means

a21 = 231