9514 1404 393
Answer:
a) 2, 5
b) no
Step-by-step explanation:
a) The terms of a sequence are numbered with the counting numbers:
1, 2, 3, 4, ...
These are the values of n for each of the successive terms of the sequence.
That is, the first term is the value of n²+1 when n=1:
1² +1 = 2
The second term of the sequence is the value of n²+1 when n=2:
2² +1 = 5
The first two terms of the sequence are 2, 5.
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b) If 35 is a term of the sequence, then there is some integer value of n such that n²+1 = 35.
The solution of this equation is ...
n² = 35 -1 = 34
n ≈ √34 ≈ 5.83
This is not an integer value, so there is no term 35 in this sequence. (However, 37 is a term.)
