Answered

At Westonci.ca, we provide reliable answers to your questions from a community of experts. Start exploring today! Discover in-depth solutions to your questions from a wide range of experts on our user-friendly Q&A platform. Join our platform to connect with experts ready to provide precise answers to your questions in different areas.


What are the next three terms in the given sequence?
3, 16, 29, 42,
A) 54, 66, 78
B)
55, 68,81
C) 1,2,3
D) 55,70,83

Sagot :

isaacaco04

Answer:

B) 55, 68,81

Step-by-step explanation:

42-29=13

29-16= 13

So 42 + 13= 55

55+ 13= 68

68+ 13= 81

semsee45

Answer:

B)  55, 68, 81

Step-by-step explanation:

Given sequence:  3, 16, 29, 42

To determine if the sequence is arithmetic or geometric, work out the difference in the terms.

[tex]\sf 3 \underset{+13}{\longrightarrow} 16 \underset{+13}{\longrightarrow} 29 \underset{+13}{\longrightarrow} 42[/tex]

This sequence adds 13 each time, so as the common difference is constant, it is an arithmetic sequence.  To find the next term in the sequence, simply add 13 to the last term:

42 + 13 = 55

55 + 13 = 68

68 + 13 = 81

Therefore, the next three terms in the given sequence are 55, 68, 81

To solve this using the general form of an arithmetic sequence:

[tex]a_n=a+(n-1)d[/tex]

where:

  • [tex]a_n[/tex] is the nth term
  • a is the first term
  • d is the common difference between terms

Given:

  • a = 3
  • d = 13

[tex]\begin{aligned}\implies a_n & =3+(n-1)13\\ & = 3+13n-13\\ & = 13n-10\end{aligned}[/tex]

Therefore, the next 3 terms in the sequence are:

[tex]\implies a_5=13(5)-10=55[/tex]

[tex]\implies a_6=13(6)-10=68[/tex]

[tex]\implies a_7=13(7)-10=81[/tex]

We hope this was helpful. Please come back whenever you need more information or answers to your queries. Thank you for your visit. We're committed to providing you with the best information available. Return anytime for more. Thank you for visiting Westonci.ca. Stay informed by coming back for more detailed answers.