Question

The 4th term of a sequence is 8 and the 6th term is 18. The sequence is either arithmetic or geometric. Which of the following can not be the 7th term?
A -27
B -23
C 23
D 27

Answer 1

Answer:

23

Step-by-step explanation:

To solve this question I have used some formula.

1. Formula to find the value of term

x + (term number - 1) × {(greater term number - smaller term number) ÷ (greater term containing value) - (smaller term containing value)}

2. Formula to find the value of x given in 1st formula

x = value containing by term - (term number - 1) × {(value containing by greater term - value containing smaller term) ÷ (6-4)}

Here greater term number means the value containing by the greater term. In this question greater term is 6 which contain a value in it that is 18. So, greater term number in this question is 18. So, smaller term number means the smaller term containing a value in it or the number containing by the greater term.

4th term = 8

To find the value of 7th term first we need to find the value of x.

              x = 8 - (4 - 1) × {(18 - 8) ÷ (6 - 4)}

              x = 8 - 3 × (10 ÷ 2)

              x = 8 - 3 × 5

              x = 8 - 15

              x = -7

Now, to check whether the value of x is -7, I have find the 4th term by replacing x with -7 in the 1st formula.

              = -7 + (4 - 1) × {(18 - 8)} ÷ (6 - 4)

              = -7 + 3 × (10 ÷ 2)

              = -7 + 3 × 5

              = -7 + 15

              = 8

Answer came 8 and its correct answer. So, the value of x is -7

I have also find the 6th term so you understand it more properly.

6th term = 18

              = -7 + (6 - 1) × [{(18 - 8)} ÷ (6 - 4)]

              = -7 + 5 × {(10 ÷ 2)}

              = -7 + 5 × 5

              = -7 + 25

              = 18

Answer of 6th term is also correct.

I think now you know how to find the 7th term.

7th term = -7 + (7 - 1) × {(18 - 8) ÷ (6 - 4)

              = -7 + 6 × (10 ÷ 2)

              = -7 + 6 × 5

              = -7 + 30

              = 23

If you think that I have made mistake anywhere or you did not understood my explanation than please ask me in comment or you can report this answer. But, before reporting please see carefully because, once any answer got reported you can't undo it.