Question 123
An arithmetic progression, usually called an A.P., is a sequence in which each term, starting from the second, equals the sum of the previous term and a fixed value $r$ called the common difference of the progression. For example, the sequence below is an arithmetic progression with first term 3 and common difference 4.
$$
a_{1}=3, a_{2}=7, a_{3}=11, a_{4}=15, a_{5}=19, a_{6}=23, a_{7}=27, a_{8}=31, a_{9}=35, \ldots
$$
Note that we denote the term in position $i$ by the symbol $a_{i}$.
a) If the first term of an arithmetic progression is 2 and its common difference is 3, what is the value of the fourth term?
b) João's teacher asked him to compute the eleventh term of an arithmetic progression. Unfortunately he forgot the first term and the common difference. The only information he remembered was:
$$
\begin{aligned}
a_{4}+a_{7}+a_{10} & =207 \\
a_{5}+a_{6}+a_{7}+a_{8}+a_{9}+a_{10}+a_{11} & =553
\end{aligned}
$$
What is the value of the eleventh term?
$$
a_{1}=3, a_{2}=7, a_{3}=11, a_{4}=15, a_{5}=19, a_{6}=23, a_{7}=27, a_{8}=31, a_{9}=35, \ldots
$$
Note that we denote the term in position $i$ by the symbol $a_{i}$.
a) If the first term of an arithmetic progression is 2 and its common difference is 3, what is the value of the fourth term?
b) João's teacher asked him to compute the eleventh term of an arithmetic progression. Unfortunately he forgot the first term and the common difference. The only information he remembered was:
$$
\begin{aligned}
a_{4}+a_{7}+a_{10} & =207 \\
a_{5}+a_{6}+a_{7}+a_{8}+a_{9}+a_{10}+a_{11} & =553
\end{aligned}
$$
What is the value of the eleventh term?