Natasha Awada, Paul La Rondie, Laurie Buchanan and, Jill Stevens Solutions for Chapter: From Patterns to Generalizations: Sequences and Series, Exercise 20: Exercise 1E

Given an arithmetic progression with $u_{21}=65$ and $d=-2$, find the value of the first term.

Given that two terms of an arithmetic sequence are $u_5=-3.7$ and $u_{15}=-52.3$, find the value of the $19\mathrm{th}$ term.

Given an arithmetic sequence in which $u_1=11$ and $d=-3$, find the term that has a value of $2$.

There exists an arithmetic sequence with $t_3=4$ and $t_6=184$. Find the $14\mathrm{th}$ term.

Find the number of terms in the finite arithmetic sequence $6,-1,-8,\dots ,-36$.

A movie theatre with $12$ rows of seating has $30$ seats in the first row. Each row behind it has two additional seats. How many seats are in the last row$?$

The Winter Olympics are held every four years and were held in Vancouver, Canada in $2010$. When will the Winter Olympics be held for the first time after $2050?$

Yinting wants to start adding weight lifting to her exercise routine. Her trainer suggest that she starts with $40$ repetitions for the first week and then increases by six repetitions each week after. Find the number of weeks before Yinting will be doing $82$ repetitions.