Question

Find the first 4 terms where the rule given is that start at 17.3 and add 0.9.

Answer 1

Analyze the question. The question states the rule: Start at 17.3 and add 0.9, which means the first term here is given and a common difference is also given. We have the first term and the common difference; thus, we have a question of arithmetic progression.

Complete step by step solution:
From the question we get the following data;
First term, a = 17.3
Common difference, d = 0.9
Thus, we know that there is an arithmetic progression in question.
To find the nth term of an arithmetic progression we use the formula,
${a_n} = a + (n - 1)d$, where n is the number of the term we need to find.
We need to find 3 more terms so,
${a_2} = a + (2 - 1)d = 17.3 + 0.9 = 18.2$
$\Rightarrow{a_3} = a + (3 - 1)d = 17.3 + 2 \times 0.9 = 19.1$
$\Rightarrow {a_4} = a + (4 - 1)d = 17.3 + 3 \times 0.9 = 20.0$

Therefore, the terms are 17.3, 18.2, 19.1 and 20.0.

Note: A progression or arithmetic sequence could be a sequence of numbers such that the difference between the consecutive terms is constant. As an example, the sequence 5, 7, 9, 11, 13, 15.... is an A.P with a common difference of two. When the common ratio between two consecutive terms in a series is the same, that sequence is called a geometric progression. Sometimes a series might not be a G.P or an A.P either. In those kinds of questions, check the common difference of the given terms, it is possible that the common difference of the terms is an A.P.