The nth term of a sequence is n^2+n

The nth term of a sequence is n^2+n
Two consecutive terms in the sequence have a difference of 32.
Work out the two terms.

Thank you!!

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Try factor out the nth term formula, what do you notice?
Try factor out the nth term formula, what do you notice?

n(n+1)??
I don't notice anything. 😱😱😱
n+1th term minus nth term set to 32 and solve.
Original post by sweetstars
The nth term of a sequence is n^2+n
Two consecutive terms in the sequence have a difference of 32.
Work out the two terms.

Thank you!!

Two consecutive terms are $n$ and $n+1$. We are looking for a pair so that the difference is 32. This means we can formulate $[(n+1)^2 +(n+1)] - [n^2 + n] = 32$
Original post by sweetstars
n(n+1)??
I don't notice anything. 😱😱😱

It means that a term of a sequence is found by multiplying it by number right after it. Eg: the 7th term is found by multiplying 7 and 8. Can you now work out how to do it?
Original post by RDKGames
Two consecutive terms are $n$ and $n+1$. We are looking for a pair so that the difference is 32. This means we can formulate $[(n+1)^2 +(n+1)] - [n^2 + n] = 32$

Aren't the contents of the first brackets multiplied instead of summed?
Aren't the contents of the first brackets multiplied instead of summed?

Why would they be multiplied?
Original post by RDKGames
Two consecutive terms are $n$ and $n+1$. We are looking for a pair so that the difference is 32. This means we can formulate $[(n+1)^2 +(n+1)] - [n^2 + n] = 32$

Also, Im pretty sure it should be (n+1)(n+2)-n (n+1)
Also, Im pretty sure it should be (n+1)(n+2)-n (n+1)

Yes my LHS factorises to this.
Original post by RDKGames
Why would they be multiplied?

Nvm ignore me, you're right.
It means that a term of a sequence is found by multiplying it by number right after it. Eg: the 7th term is found by multiplying 7 and 8. Can you now work out how to do it?

Please, another clue thank you. I don't get it...
Original post by sweetstars
Please, another clue thank you. I don't get it...

Have you tried what I said?
Nvm ignore me, you're right.

Wait so which is the correct formula?
Original post by sweetstars
The nth term of a sequence is n^2+n
Two consecutive terms in the sequence have a difference of 32.
Work out the two terms.

Thank you!!

let's say the first term if the two consecutive numbers is n. this means that's the next number is n+1.
now since the difference is 32,we can say;
nth term - (n+1)th term = 32
And we r givene the formula to calculate the nth term of the sequence so;
n (n+1) - (n+1)(n+1+1) = 32
n(n+1)-(n+1)(n+2) = 32.
Can u do it from here ?
Original post by brainmaster
let's say the first term if the two consecutive numbers is n. this means that's the next number is n+1.
now since the difference is 32,we can say;
nth term - (n+1)th term = 32
And we r givene the formula to calculate the nth term of the sequence so;
n (n+1) - (n+1)(n+1+1) = 32
n(n+1)-(n+1)(n+2) = 32.
Can u do it from here ?

You mean (n+1)th term minus nth term, not other way around
Original post by RDKGames
Have you tried what I said?

Is it 15 and 16?
Original post by sweetstars
Is it 15 and 16?

Yep.
Original post by RDKGames
Yep.

Thank you very much!
Original post by RichE
You mean (n+1)th term minus nth term, not other way around

yes thanks for that.
however we could also use nth term - (n+1)th term = 32
but u get n as -15 and we know n can never be a negative hence u ignore the negative.