For the sequence a1,a2,a3,, an,an=an1+an2 for all values n2. If a1

Question

For the sequence  a_{1}, a_{2}, a_{3} , ...,  a_{n}, a_{n} = a_{n−1} + a_{n−2}  for all values  n>2 . If  a_{1} = 1  and  a_{3} = 4 , what are the values of  a_{2}  and  a_{8} ?

GmatTest2026 · Answer

Solution:

As we know n>2, a1=1, a3=4

Here we go: a3 = a2 + a1 ---> 4 = a2 + 1 = 3
 a4 = a3 + a2----> 4 + 3 = 7
 a5 = a4 + a3----> 7 + 4 = 4
 a6 = a5 + a4----->11+7 = 18
 a7 = a6 + a5----->18+11= 29
 a8 = a7 + a6----->29+18=47

So, a2 = 3 and a8 = 47

Bismuth83 · Answer

1. We are asked to  figure out the values of two specific terms in a given sequence .

2. The recursive identity has three consecutive terms, which means figuring out 3 neighboring terms will give us the whole sequence.

3. Since  a_1  and  a_3  are given, using our logic, it's best to find  a_2 :  a_3 = a_2 + a_1 \rightarrow 4 = a_2 + 1 \rightarrow a_2 = 3 .

4. Now we can find the following terms.

-  a_4 = a_3 + a_2 = 4 + 3 = 7 .
 -  a_5 = a_4 + a_3 = 7 + 4 = 11 .
 -  a_6 = a_5 + a_4 = 11 + 7 = 18 .
 -  a_7 = a_6 + a_5 = 18 + 11 = 29 .
 -  a_8 = a_7 + a_6 = 29 + 18 = 47 .

5. Our answer will be:  a_2 = 3  and  a_3 = 47 .

\(a_2\)	\(a_8\)	Answer values
		2
		3
		29
		47
		76

For the sequence a1,a2,a3,, an,an=an1+an2 for all values n>2. If a1

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