# Which arithmetic sequence contains the term 34?

Arithmetic and Geometric progressions.

### Which arithmetic sequence contains the term 34?

Which arithmetic sequence contains the term 34?
1. t=6+(n-1)4
2. t=3n-1

1 or 2 ?

Math Tutor

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### Re: Which arithmetic sequence contains the term 34?

Solution: Given the arithmetic sequences Tn= 6+(n-1)4
by AP we have Tn=a+(n-1)d
a=6
d=4

34=6+(n-1)4
n=8

8th term contain 34.

Jonasmathwork

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### Re: Which arithmetic sequence contains the term 34?

First arithmetic sequence contains the term 34
t=6+(n-1)4

leesajohnson

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### Re: Which arithmetic sequence contains the term 34?

There are numerous arithmetic progressions where 34 in a term in the sequence.

Any sequence that satisfies the equation a + (n-1)d = 34

If take starting value of 1 and common difference of 1 then 34 is there...

1 + (n-1)*1 = 34
n = 34 .....the 34th term is 34.

If take starting value of 1 and common difference of 2 then 34 is NOT there...

1 + (n-1)*2 = 34
1 + 2n - 2 = 34
2n = 34 + 1
2n = 35
n = 17.5 ... n is not an even number so 34 is NOT there.

If take starting value of 1 and common difference of 3 then 34 is there...

1 + (n-1)*3 = 34
1 + 3n - 3 = 34
3n = 34 + 2
3n = 36
n = 12 ....so 34 is the 12th term in the sequence.

If take starting value of 2 and common difference of 2 then 34 is there...

2 + (n-1)*2 = 34
2 + 2n - 2 = 34
2n = 34
2n = 34
n = 17 ....so 34 is the 17th term in the sequence.

If take starting value of 2 and common difference of 3 then 34 is there...

2 + (n-1)*3 = 34
2 + 3n - 3 = 34
3n = 34 + 1
3n = 35
n = 11.66 .... n is not an even number so 34 is NOT there.

If take starting value of 2 and common difference of 4 then 34 is there...

2 + (n-1)*4 = 34
2 + 4n - 4 = 34
4n = 34 + 2
4n = 36
n = 9 ....so 34 is the 9th term in the sequence.

.....so there are lots and more............

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