Resourcesdown chevron
Testimonials
Plans
Sign in
Sign up
Resourcesright arrow
Testimonials
Plans
Bytelearn - cat image with glassesAI tutor

Welcome to Bytelearn!

Let’s check out your problem:

Find the first five terms of the sequence defined below, where nn represents the position of a term in the sequence. Start with n=1n = 1.\newlinean=2(4)na_n = 2(4)^n\newline_____, _____, _____, _____, _____

View step-by-step helpView step-by-step help
Homeright chevron icon
Math Problemsright chevron icon
Algebra 2right chevron icon
Evaluate explicit formulas for sequencesright chevron icon

Full solution

Q. Find the first five terms of the sequence defined below, where nn represents the position of a term in the sequence. Start with n=1n = 1.\newlinean=2(4)na_n = 2(4)^n\newline_____, _____, _____, _____, _____
  1. Find First Term: To find the first term of the sequence, substitute n=1n = 1 into the formula an=2(4)na_n = 2(4)^n.\newlineCalculation: a1=2(4)1=2×4=8a_1 = 2(4)^1 = 2 \times 4 = 8
  2. Find Second Term: To find the second term of the sequence, substitute n=2n = 2 into the formula an=2(4)na_n = 2(4)^n.\newlineCalculation: a2=2(4)2=2×16=32a_2 = 2(4)^2 = 2 \times 16 = 32
  3. Find Third Term: To find the third term of the sequence, substitute n=3n = 3 into the formula an=2(4)na_n = 2(4)^n.\newlineCalculation: a3=2(4)3=2×64=128a_3 = 2(4)^3 = 2 \times 64 = 128
  4. Find Fourth Term: To find the fourth term of the sequence, substitute n=4n = 4 into the formula an=2(4)na_n = 2(4)^n.\newlineCalculation: a4=2(4)4=2×256=512a_4 = 2(4)^4 = 2 \times 256 = 512
  5. Find Fifth Term: To find the fifth term of the sequence, substitute n=5n = 5 into the formula an=2(4)na_n = 2(4)^n.\newlineCalculation: a5=2(4)5=2×1024=2048a_5 = 2(4)^5 = 2 \times 1024 = 2048

More problems from Evaluate explicit formulas for sequences

Question
Find the sum of the finite arithmetic series. ∑n=110(7n+4)\sum_{n=1}^{10} (7n+4)\newline______
Get tutor helpright-arrow

Posted 2 months ago

Question
Type the missing number in this sequence: `55,\59,\63,\text{_____},\71,\75,\79`
Get tutor helpright-arrow

Posted 1 month ago

Question
Type the missing number in this sequence: `2, 4 8`, ______,`32`
Get tutor helpright-arrow

Posted 2 months ago

Question
What kind of sequence is this? 2,10,50,250,…2, 10, 50, 250, \ldots Choices:Choices:\newline[A]arithmetic\text{[A]arithmetic}\newline[B]geometric\text{[B]geometric}\newline[C]both\text{[C]both}\newline[D]neither\text{[D]neither}
Get tutor helpright-arrow

Posted 2 months ago

Question
What is the missing number in this pattern? 1,4,9,16,25,36,49,64,81,____1, 4, 9, 16, 25, 36, 49, 64, 81, \_\_\_\_
Get tutor helpright-arrow

Posted 1 month ago

Question
Classify the series. ∑n=012(n+2)3 \sum_{n = 0}^{12} (n + 2)^3 \newlineChoices:\newline[A]arithmetic\text{[A]arithmetic}\newline[B]geometric\text{[B]geometric}\newline[C]both\text{[C]both}\newline[D]neither\text{[D]neither}
Get tutor helpright-arrow

Posted 1 month ago

Question
Find the first three partial sums of the series.\newline1+6+11+16+21+26+⋯1 + 6 + 11 + 16 + 21 + 26 + \cdots\newlineWrite your answers as integers or fractions in simplest form.\newlineS1=S_1 = ____\newlineS2=S_2 = ____\newlineS3=S_3 = ____
Get tutor helpright-arrow

Posted 1 month ago

Question
Find the third partial sum of the series. \newline3+9+15+21+27+33+⋯3 + 9 + 15 + 21 + 27 + 33 + \cdots\newlineWrite your answer as an integer or a fraction in simplest form. \newlineS3=S_3 = ____
Get tutor helpright-arrow

Posted 1 month ago

Question
Find the first three partial sums of the series. \newline1+7+13+19+25+31+⋯1 + 7 + 13 + 19 + 25 + 31 + \cdots\newlineWrite your answers as integers or fractions in simplest form. \newlineS1=S_1 = ____\newlineS2=S_2 = ____\newlineS3=S_3 = ____
Get tutor helpright-arrow

Posted 2 months ago

Question
Does the infinite geometric series converge or diverge?\newline1+34+916+2764+⋯1 + \frac{3}{4} + \frac{9}{16} + \frac{27}{64} + \cdots\newlineChoices:\newline[A]converge\text{[A]converge}\newline[B]diverge\text{[B]diverge}
Get tutor helpright-arrow

Posted 1 month ago

View all (11)