Question

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

Answer 1

B) 55, 68,81

Explanation:

42-29=13

29-16= 13

So 42 + 13= 55

55+ 13= 68

68+ 13= 81

Answer 2

B) 55, 68, 81

Explanation:

Given sequence: 3, 16, 29, 42

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

`\sf 3 \underset{+13}{\longrightarrow} 16 \underset{+13}{\longrightarrow} 29 \underset{+13}{\longrightarrow} 42`

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:

`a_n=a+(n-1)d`

where:

• 
  `a_n` is the nth term
• a is the first term
• d is the common difference between terms

Given:

• a = 3
• d = 13

`\begin{aligned}\implies a_n & =3+(n-1)13\\ & = 3+13n-13\\ & = 13n-10\end{aligned}`

Therefore, the next 3 terms in the sequence are:

`\implies a_5=13(5)-10=55`

`\implies a_6=13(6)-10=68`

`\implies a_7=13(7)-10=81`