Find the nth term of the sequence 7,11,15,19...

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The nth term is a formula that allows us to find the value of a term in a sequence given its position in the sequence, whether this is the second term (n=2) or the millionth (n=1000000). 

In the above sequence, there is a difference of four between each term: 11-7=4, 15-11=4, etc. This means that the nth term is going to look something like 4n+6, or 4n-3, but we need to be sure of the number we are adding or subtracting at the end. The first term (n=1) is seven. So we know that 4(1) + *something* = 7

4(1)=4x1=4

4+*something*=7

and subtracting 4 from both sides gives us 3. So the nth term is 4n+3. To check our answer, we can check another term. The fourth term (n=4) is 19, so putting n=4 in our formula should give 19.

fourth term = 4(4)+3

=16+3

=19, which is what we wanted, so we can be sure that the nth term is indeed 4n+3.

Joe B. GCSE Maths tutor, A Level Maths tutor, GCSE Further Mathematic...

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