Show thet the followiong sequences is an A.P. Also, find the comm… - Vidyadip

Question

Show thet the followiong sequences is an A.P. Also, find the common difference and write 3 more terms in each case. $3,-1,-5,-9...$

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Answer

$3,-1,-5,-9...$ $\text{a}_1=3,\text{a}_2=-1,\text{a}_3=-5,\text{a}_4=-4$ $\text{a}_2-\text{a}_1=-1-3=-4$ $\text{a}_3-\text{a}_2=-5-(-1)=-4$ $\text{a}_4-\text{a}_3-=9(-5)=-4$ $\therefore$ common difirence is $=-4$ $\text{a}_4-\text{a}_3=\text{a}_3-\text{a}_2=\text{a}$ $\therefore$ The given sequerence is a A.P $\therefore\text{a}_5=3+(5-1)(-4)=-13$ $\text{a}_6=3+(6-1)(-4)=-17$ $\text{a}_7=3+(7-1)(-4)=-21$

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