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Arithmetic Progressions — Maths STD 10 — Question

Maharashtra BoardEnglish MediumSTD 10MathsArithmetic Progressions2 Marks
Question
Write the first five terms of the following sequences whose $n^{th}$​​​​​​​ terms are:
$\text{a}_\text{n}=\frac{2\text{n}-3}{6}$
✓

Answer

Given sequence is, $\text{a}_\text{n}=\frac{2\text{n}-3}{6}$
To write first five terms of given sequence we put $n = 1, 2, 3, 4, 5.$ Then, we get,
$\text{a}_1=\frac{2.1-3}{6}=\frac{2-3}{6}=\frac{-1}{6}$
$\text{a}_2=\frac{2.2-3}{6}=\frac{4-3}{6}=\frac{1}{6}$
$\text{a}_3=\frac{2.3-3}{6}=\frac{6-3}{3}=\frac{1}{2}$
$\text{a}_4=\frac{2.4-3}{6}=\frac{8-3}{6}=\frac{5}{6}$
$\text{a}_5=\frac{2.5-3}{6}=\frac{10-3}{6}=\frac{7}{6}$
$\therefore$ The required first five terms of given sequence $\text{a}_\text{n}-\frac{2_\text{n}-3}{6}$ are $\frac{-1}{6},\frac{1}{6},\frac{1}{2},\frac{5}{6},\frac{7}{6}.$

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