સમાંતર શ્રેણી 18, 16.5, 15, ... નું n મુ પદ શોધો.
Understand the Problem
આ પ્રશ્ન એક સમાંતર શ્રેણી આપી છે અને આ સમાંતર શ્રેણી નું n મુ પદ શોધવાનું કહે છે. એટલે કે શ્રેણીના nમા સ્થાન પર કઈ સંખ્યા આવે તે શોધવાનું છે.
Answer
$a_n = 19.5 - 1.5n$
Answer for screen readers
$a_n = 19.5 - 1.5n$
Steps to Solve
- Find the common difference $d$
The common difference $d$ is the difference between consecutive terms in the arithmetic sequence. $d$ = 16.5 - 18 = -1.5
- Substitute the values of $a$ and $d$ into the formula
The formula general term of an arithmetic sequence is given by $a_n = a + (n-1)d$, where $a$ is the first term, $d$ is the common difference, and $n$ is the term number. Here, $a = 18$ and $d = -1.5$. Substituting these values into the formula for the $n$th term: $a_n = 18 + (n-1)(-1.5)$.
- Simplify the expression
Now we simplify the expression
$a_n = 18 -1.5(n-1)$ $a_n = 18 -1.5n + 1.5$ $a_n = 19.5 - 1.5n$
$a_n = 19.5 - 1.5n$
More Information
The $n$th term of the given arithmetic sequence is $19.5 - 1.5n$.
Tips
A common mistake when finding the $n$th term of an arithmetic sequence is incorrectly calculating the common difference $d$. Also, distributing the common difference to both terms inside the parentheses $(n-1)$ i.e. $-1.5$ to both $n$ and $-1$
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