Question

the terms in the sequence increase by the same amount each time ? ? 17 ? ? 29 a)work out the missing terms b)work out in terms of n the nth term of the sequence

Answer 1

Answer:

The missing terms are 9,13,21 and 25

The nth term is 4n + 5

Step-by-step explanation:

From the arrangement, we can see that 17 is the third term while 29 is the 6th term

Now is this sequence arithmetic or geometric?

Since it increases by the same amount each time, then it is an arithmetic sequence.

Mathematically the third term in an arithmetic sequence with first term a and common difference d is ;

a + 2d = 17 •••••(i)

While for the sixth term, we have

a + 5d = 29 ••••••(ii)

The equations are obtainable for the nth term of an arithmetic sequence which can be written as;

Tn = a + (n-1)d

where a is the first term, n is the term number and d is the common difference

Now solving both equations simultaneously;

We can subtract equation i from ii

Thus;

5d-2d = 29-17

3d= 12

d = 12/3 = 4

we can substitute the value of d in any of the equations to get a

let’s use 1

That would be;

a + 2d= 17

a + 2(4) = 17

a + 8 = 17

a = 17-8

a = 9

Now the first term is 9

Second would be 9 + 4 = 13

Fourth would be 3rd + d = 17 + 4 = 21

Fifth would be 4th + d = 21 + 4 = 25

So the sequence now correctly arranged would be;

9,13,17,21,25,29

where 9,13,21 and 25 are the missing terms

b. Mathematically the nth term of the sequence is

a + (n-1)d

let’s substitute the values of a and d , we have

9 +(n-1)4

9 + 4n-4

4n + 5