Rule 1: Multiply by 2, then add one third starting from 1. Rule 2: Add one half, then multiply by 4 starting from 0. What is the fourth ordered pair using the two sequences?
A) (two and one third, 2)
B)(four and two thirds, 42)
C)(5, 10)
D)(10, ten and one half)
Answers
c) correct option
this is right answer
Correct options:
A) (two and one third, 2)
B) (ten and one third, 42)
C) (5, 10)
D) (10, ten and one half)
Answer:
The fourth ordered pair using the two sequences is B) (ten and one-third, 42).
Step-by-step explanation:
The first sequence is given as multiplying the terms by 2 and then adding one-third. The sequence starts from 0.
a₁ = 1
a₂ = (2×1) + 1/3 = 2 + 1/3 = 7/3
a₃ = (2×7/3) + 1/3 = 14/3 + 1/3 = 5
a₄ = (2×5) + 1/3 = 10 + 1/3 = 31/3 = 10(1/3)
Hence, the sequence is 1, 7/3, 5, 31/3, ...
The second sequence is given by adding one half and then multiplying by 4. The sequence starts from 0.
a₁ = 0
a₂ = (0+1/2) × 4 = 2
a₃ = (2+1/2) × 4 = 5/2 × 4 =10
a₄ = (10 + 1/2) × 4 = 21/2 × 4 = 42
Hence, the sequence is 0, 2, 10, 42, ...
Therefore, the fourth terms of the two sequences are ten and one-third [10(1/3)] and 42 respectively.
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