SEQUENCES AND SERIES — MATHS STD 11 Science — Question
Gujarat BoardEnglish MediumSTD 11 ScienceMATHSSEQUENCES AND SERIES1 Mark
Question
Write the first five terms of the sequence and obtain the corresponding series $a_1 = a_2 = 2, a_n = a_{n-1} - 1, n > 2$.
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Answer
Given: $a_1=a_2=2, a_n=a_{n-1}-1, n>2$
Putting $n=3,4$ and 5 , we get
$a_3=a_{3-1}-1=a_{2-1}=2-1=1$
$a_4=a_{4-1}-1=a_{3-1}=1-1=0$
$a_5=a_{5-1}-1=a_{4-1}=0-1=-1$
Hence the first five terms are $2,2,1,0,-1$.
Therefore, corresponding series is $2+2+1+0+(-1)+\ldots . .$.
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