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Arithmetic Progressions — Maths STD 10 — Question

CBSE BoardEnglish MediumSTD 10MathsArithmetic Progressions3 Marks
Question
Find the indicated terms in the following sequences whose $n^{th}$ terms are:
$\text{a}_\text{n}=\frac{3\text{n}-2}{4\text{n}+5};\text{a}_7\text{ and }\text{a}_8$
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Answer

$\text{a}_\text{n}=\frac{3\text{n}-2}{4\text{n}+5}$
We need to find $a_7$ and $a_8$
Now, to find $a_7​​​​​​​$​​​​​​​ term we use $n = 7$, we get,
$\text{a}_7=\frac{3(7)-2}{4(7)+5}$
$=\frac{21-2}{28+5}$
$=\frac{19}{33}$
Also, to find $a_8​​​​​​​$​​​​​​​ term we use $n = 8$, we get
$\text{a}_8=\frac{3(8)-2}{4(8)+5}$
$=\frac{24-2}{32+5}$
$=\frac{22}{37}$
Thus, $\text{a}_7=\frac{19}{33}\text{ and }\text{a}_8=\frac{22}{37}$

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