Answer:
Ai. Arithmetic sequence
Aii. Tn = 5 + 7n
Bi. Geometric
Bii. Tn = 8 × 2ⁿ¯¹
Explanation:
To successfully answer the questions given above, note the following:
1. If the sequence is Arithmetic, then:
2nd – 1st = 3rd – 2nd = common difference (d)
2. If the sequence is geometric, then,
2nd / 1st = 3rd / 2nd = common ratio (r)
3. A sequence can not be arithmetic geometric at the same time.
4. The nth term of arithmetic sequence is:
Tn = a + (n – 1)d
5. The nth term of geometric sequence is:
Tn = arⁿ¯¹
A. Sequence => 12, 19, 26
i. Determination of the type of sequence.
We'll begin by calculating the common difference
1st term = 12
2nd term = 19
3rd term = 26
Common difference (d) = 2nd – 1st
d = 19 – 12 = 7
OR
d = 3rd – 2nd
d = 26 – 19 = 7
Since a common difference exist in the sequence, the sequence is arithmetic sequence.
ii. Determination of the nth term.
Common difference (d) = 7
1st term (a) = 12
nth term (Tn) =?
Tn = a + (n – 1)d
Tn = 12 + (n – 1)7
Tn = 12 + 7n – 7
Tn = 5 + 7n
B. Sequence => 8, 16, 32
Bi. Determination of the type of sequence.
Let us begin by calculating the common ratio.
1st term = 8
2nd term = 16
3rd term = 32
Common ratio (r) = 2nd / 1st
r = 16 / 8
r = 2
OR
r = 3rd / 2nd
r = 32 / 16
r = 2
Since a common ratio exist in the sequence, the sequence is geometric.
Bii. Determination of the nth term.
Common ratio(r) = 2
1st term (a) = 8
nth term =?
Tn = arⁿ¯¹
Tn = 8 × 2ⁿ¯¹