Nth term dont understand at all?

Question

i need help doing the nth term i dont get it at all!!! so please tell me everything in baby steps since i stink at alegbra too

so i need help in questions like these

for each of the following give an expression for the nth term:

a) 2, 5, 10, 17, 26...

b) -4, 4, 12, 20...

c) 3, 5, 7, 9, 11...

d) 7, 13, 19, 25, 31...

Answer 1

The nth term is a ...formula you could say, to work out any number in that general sequence.

So I'll take an easy one to explain to you.

Part c) 3, 5, 7, 9, 11

There is a general formula you can use to find your nth term.

In this case, it is "a + (n - 1)d"

a = first term

n = number of terms (we don't have this, which is why we're finding the nth term)

d = common difference (the number each is added by)

In this instance, your first term is 3, and your common difference is 2 (3 + 2 = 5, 5 + 2 = 7, 7 + 2 = 9 and so on...)

a = 3 and d = 2

Now, you put these numbers back into the equation (a + (n - 1)d ) to find your 'nth term'

nth term = 3 + (n - 1)2

Now, expand your brackets:

3 + 2n - 2

Therefore your nth term = 1 + 2n.

I hope that helps you!

Answer 2

a)difference is 3,5,7,9

       difference is 2 btw everything so we divide the 2 by 2=1 an add the first difference to n^2 since the difference btw this numbers are not linear.  (n^2+1) is the formular

  b)add 8 to all the temrs to get next one=8-12n because if u move back an subtract 8 u get the nth term (8-12n)

c)diff is 2 write 2 an then subtact 2 from the first term(3-2)=1 so 2+1n

d)diff is 6 write 6 an subtact 6 from 7 =1 then write 6+1n

Answer 3

Lets pick the easy ones first

b) starts with-4 and you add 8 to get the next

so, nth term is -4 +8(n-1)

c)is the same start at 3 and add 2

so, nth term is 3 +2(n-1)

d)is the same start at 7 and add 6

so, nth term is 7 +6(n-1)

a) is a bit more difficult. Nasty they set it first!!!

Series is  2, 5, 10, 17, 26...

Difference is 3,5,7,9 = 2n-1

And the differences of that are all 2...

So this is of the form an^2+bn+c

n=1 answer is a+b+c=2

n=2 answer is 4a+2b+c=5

n=3 answer is 9a+3b+c=10

so nth term is n^2+1

so nth is