Answer:
234
Step-by-step explanation:
Using the recursive formula with a₁ = 3
a₂ = 4a₁ + 2 = (4 × 3) + 2 = 12 + 2 = 14
a₃ = 4a₂ + 2 = (4 × 14) + 2 = 56 + 2 = 58
a₄ = 4a₃ + 2 = (4 × 58) + 2 = 232 + 2 = 234
The 4th term of the sequence is 234.
A collection of numbers with a particular pattern is called sequence.
A sequence may be either in ascending order or in descending order.
Given that, [tex]a_{1}[/tex] = 3
The given recursion formula is [tex]a_{n}=4a_{n-1}+2[/tex]
So, [tex]a_{2}=4a_{1}+2[/tex]
= 4×3+2
= 14
Now, [tex]a_{3}=4a_{2}+2[/tex]
= 4×14+2
= 58
∴ [tex]a_{4}=4a_{3}+2[/tex]
= 4×58+2
= 234
Hence, the 4th term is 234.
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