Question

Need a little help checking this question, It's out of options A or C

List the next three terms in the following sequence:

1, 9, 17, 25, 33, 41,...

the next it should give is 49, 57, 65, but I'm stuck on the last number

Answer 1

A

Explanation:

Given the sequence

1, 9, 17, 25, 33, 41

Note the difference in consecutive terms

9 - 1 = 8

17 - 9 = 8

25 - 17 = 8

33 - 25 = 8

41 - 33 = 8

Since the terms have a common difference d then the sequence is arithmetic

To obtain the next term in the sequence add 8 to the previous term

41 + 8 = 49

49 + 8 = 57

57 + 8 = 65

The next 3 terms are 49, 57, 65

The n th term of an arithmetic sequence is

`a_(n)` = a₁ + (n - 1)d

where a₁ is the first term and d the common difference, thus

`a_(20)` = 1 + (19 × 8) = 1 + 152 = 153

The required solution is 49, 57, 65 ; 153 → A

Answer 2

Answer is option A

Explanation:

Given: sequence 1, 9, 17, 25, 33, 41

Now we will find the difference in consecutive terms

9 - 1 = 8

17 - 9 = 8

25 - 17 = 8

33 - 25 = 8

41 - 33 = 8

As the difference between the terms is same, so the given sequence forms an arithmetic progression .

In order to obtain the next term in the sequence add 8 to the previous term

41 + 8 = 49

49 + 8 = 57

57 + 8 = 65

Consider the AP : 1, 9, 17, 25, 33, 41, 49, 57, 65,...

Here, difference 9 ( d ) = 9-1=8

First term ( a ) = 1

We know that nth term is given by
`a_n=a+(n-1)d`

For n = 20,

`a_(20)=1+(20-1)8=1+152=153`

So, answer is option A.