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Question Number 192991 by otchereabdullai@gmail.com last updated on 01/Jun/23
the first, third and sixth terms of a  linear sequence are the first three   terms of an exponential sequence.   find the common ratio
thefirst,thirdandsixthtermsofalinearsequencearethefirstthreetermsofanexponentialsequence.findthecommonratio
Answered by MM42 last updated on 01/Jun/23
l.s : t_1  , t_3   , t_6     ; t_n =t_1 +(n−1)d  e.s: a_1  , a_(2 ) , a_3     ; a_n =a_1 q^(n−1)   a_1 =t_1  &  a_2 =t_3 =t_1 +2d  &  a_3 =t_6 =t_1 +5d  a_1 ×a_3 =(a_2 )^2 ⇒t_1 =4d  ⇒a_1 =4d  &  a_2 =6d  &  a_3 =9d  ⇒q=(3/2) ✓
l.s:t1,t3,t6;tn=t1+(n1)de.s:a1,a2,a3;an=a1qn1a1=t1&a2=t3=t1+2d&a3=t6=t1+5da1×a3=(a2)2t1=4da1=4d&a2=6d&a3=9dq=32
Commented by otchereabdullai@gmail.com last updated on 01/Jun/23
thanks
thanks

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