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Arithmetic Progressions — MATHS STD 11 Science — Question

Gujarat BoardEnglish MediumSTD 11 ScienceMATHSArithmetic Progressions2 Marks
Question
Write the first five terms in the following sequences:$​​\text{a}_1=1=​​\text{a}_2,​​\text{a}_\text{n}=\ ​\text{a}_{\text{n}-1}+​​\text{a}_{\text{n}-2},​​\text{n}>2$
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Answer

$​​\text{a}_1=​​\text{a}_2=1$ $​​\text{a}_\text{n}=​​\text{a}_{\text{n}-1}+\text{a}_{\text{n}-2}\ \text{n}>2$ $\Rightarrow\text{a}_3=\text{a}_{3-1}+\text{a}_{3-2}$ $=\text{a}_2+\text{a}_1=1+1=2$ $\Rightarrow\text{a}_4=\text{a}_{4-1}+\text{a}_{4-2}$ $=\text{a}_3+\text{a}_2=2+1=3$ $\Rightarrow\text{a}_5=\text{a}_{5-1}+\text{a}_{5-2}$ $=\text{a}_4+\text{a}_3=5$$\therefore$ The given sequence is 1, 1, 3, 5.

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