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