Question

Please help! 100points! A sequence is defined recursively by the given formulas. Find the first five terms of the sequence.

an = 2(an − 1 + 4) and a1 = 5 (the n and n-1 is suppose to be a subscript, I just can't figure out how to make it like that)

Answer 1

5, 18, 44, 96, 200

Explanation:

Given

• aₙ = 2(aₙ₋₁ + 4)
• a₁ = 5

First term : 5

Second term : a₂ = 2(a₁ + 4)

• a₂ = 2(5 + 4) = 2(9) = 18

Third term : a₃ = 2(a₂ + 4) = 2(18 + 4) = 2(22) = 44

Fourth term : a₄ = 2(a₃ + 4) = 2(44 + 4) = 2(48) = 96

Fifth term : a₅ = 2(a₄ + 4) = 2(96 + 4) = 2(100) = 200

Hence, the first 5 terms of the sequence are :

• 5, 18, 44, 96, 200

Answer 2

5, 18, 44, 96, 200

Explanation:

`\textsf{Given sequence}: \quad a_n=2(a_(n-1)+4)`

`\textsf{Given first term}: \quad a_1=5`

`\implies a_1=5`

`\implies a_2=2(a_(1)+4)=2(5+4)=2(9)=18`

`\implies a_3=2(a_(2)+4)=2(18+4)=2(22)=44`

`\implies a_4=2(a_(3)+4)=2(44+4)=2(48)=96`

`\implies a_5=2(a_(4)+4)=2(96+4)=2(100)=200`