The given formula means that, after the first two terms of the sequence, every term a_(n+2) is the sum of two previous terms a_(n+1) and a_n, the second of which is multiplied by 2.
a_1&=7
a_2&=10
a_(n+2)&=2a_n+a_(n+1)
To do so, we will use a table. To find a_3 we will substitute 1 for n in the above formula. To find a_4 we will substitute 2 for n, and so on.
n
a_(n+2)=2a_n+a_(n+1)
2a_n+a_(n+1)
a_(n+2)
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a_1= 7
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a_2= 10
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1
a_(1+2)=2a_1+a_(1+1) ⇕ a_3=2a_1+a_2
a_3=2 a_1+ a_2 ⇓ a_3=2( 7)+ 10
a_3= 24
2
a_(2+2)=2a_2+a_(2+1) ⇕ a_4=2a_2+a_3
a_4=2 a_2+ a_3 ⇓ a_4=2( 10)+ 24
a_4= 44
3
a_(3+2)=2a_3+a_(3+1) ⇕ a_5=2a_3+a_4
a_5=2 a_3+ a_4 ⇓ a_5=2( 24)+ 44
a_5= 92
The first five terms of the sequence are 7, 10, 24, 44, and 92.
