Question

Prepare a sequence of remainders when pentagonal numbers are divided by 2 and find sum of first 50 terms of new sequence.

please answer the question in full solution and i will mark you as brainliest and give 100 points. ​

Answer 1

Step-by-step explanation:

The nth pentagonal number pn is defined algebraically as pn=n(3n−1)2 for n≥1. It can also be defined visually as the number of dots that can be arranged evenly in a pentagon

Visual representation of pentagonal numbers

Since in the visual representation of pn, the pentagon has n+1 dots on each side, counting the number of dots on each side and multiplying by 5, we get, 5(n+1). However, we have counted the dots at the vertices twice, so we subtract 5: which gives us pn=5n. Why does this not correspond to the algebraic definition?♥️♥️

Answer 2

Step-by-step explanation:

Let y = 100

Then reduction = 20% = 20

Then x = 100 – 20 = 80

(i)x/y = 80/100 = 4/5 (Diving by 20)

(ii) (y – x)/y = (100 – 80)/100

= 20/100

= 1/5 (Dividing by 20)

(iii) x/(y – x)

= 80/(100 – 80)

= 80/20

= 4/1 = 4 (Dividing by 20)