Question

Write 3 examples for finite arithmetic progression and 3 for infinite

Answer 1

Step-by-step explanation:

A simple arithmetic sequence is when a=1 and d=1, which is the sequence of positive integers:

Tn∴{Tn}=a+(n−1)d=1+(n−1)(1)=n=1;2;3;4;5;…

If we wish to sum this sequence from n=1 to any positive integer, for example 100, we would write

∑n=1100n=1+2+3+⋯+100

S100+S100−−−−∴2S100∴2S100∴S100=1+2+3+⋯+98+99+100=100+99+98+⋯+3+2+1−−−−−−−−−−−−−−−−−−−−−−−−−−−−=101+101+101+⋯+101+101+101=101×100=10 100=10 1002=5 050

we can calculate the sum S20 for the arithmetic sequence Tn=3+7(n−1) by summing all the individual terms:

S20=∑n=120[3+7(n−1)]=3+10+17+24+31+38+45+52+59+66+73+80+87+94+101+108+115+122+129+136=1390