Use the arithmetic sequence of numbers 2, 4, 6, 8, 10. Using the formula for the nth term of an arithmetic?

Question

sequence, what is 101st term, 20th term, and 30th term? Please show me how to do this.

Answer 1

It is = 2n

n = [1,inf]

1st term is, 2 x 1 = 2
2nd term is 2 x2 = 4
3rd term is 2 x 3 = 6
......
20th term is 2 x 20 = 40
.....
30th term is 2 x 30 = 60
....
101 th term is 2 x 101 = 202
.... and so on

Answer 2

just to let you know you asked the question wrong. it should be writen:
Using the formula for the nth term of an arithmetic sequence, what is 101st
Using the formula for the sum of an arithmetic series, what is the sum of the first 20 terms?
Using the formula for the sum of an arithmetic series, what is the sum of the first 30 terms?

so the answers i get for each are as followed
first part

a1 = 2 (first number in the sequence)
N = 101 (101st term)
d = 2 (the number we get from the ratio of 2,4,6,8,10....)

a101 = a1 + (n-1)d
a101 = 2+(101-1)2
a101 = 2+(100)2
a101 = 202

2nd part
we need to find what the value of the 20th term is to get the sum of a sequence. so we will use the same formula as above.

a1 = 2
n = 20
d = 2

a20 = a1 + (n-1)d
a20 = 2+(20-1)2
a20 = 2+(19)2
a20 = 40

Ok, so we now know that the 20th term equals 40. We can use that value in are next formula to get the sum of all 20 terms.

s20 = 20(2+40 / 2)
s20 = 20(42 / 2 )
s20 = 20(42 / 2)
s20 = 20(21)
s20 = 420
so the sum of the first 20 terms = 420

i dont want give away all the fun so ill leave the 3rd example up to you. hope this is helpful. well here is a small hint

a1 = 2
n = 30
d = 2

Answer 3

look at the sequence and see that for n = 3 the number is 6, for n = 5 the number is 10 so for n = 101 the number must be 202 for n = 20 the number must be 40 and so on, thus the nth term must be 2 times n.

the 30th term must be 2*30 = 60

Answer 4

Some of the previous answers are right but explanations are a bit confusing, it can be easily done with the help of A.P. formula :

tn = a + [(n - 1)*d]
where,
tn = nth. term of A.P. series
a = 1st. term in that series
d = common difference

Now, coming to ur question --
in sequence 2,4,6,8,10, ...,
a = 2,
d = (4-2) = (6-4) = (8-6) = ... = 2
so,
101st term = 2 + [(101 - 1)*2] = 202
20th term = 2 + [(20 - 1)*2] = 40
30th term = 2 + [(30 - 1)*2] = 60

Answer 5

The formula is
y(n) = n*2

or in plain language, the nth term [y sub n] of the sequence is n*2. To solve, just plug the number of the term (101, 20, 30, etc) into the equation to get what the term will be.

Answer 6

Term 1 is 2
Term 2 is 4
Term 3 is 6, etc
Each value is 2 times the term i.e the 5th term is 2*5 or 10.
the 101th term is 101 * 2 or 202
the 20th is 2*20 or 40, etc.

Answer 7

first term a =2

common difference = 2 try 4-2 or 6-4 or 8-6

nth term tn = a + (n-1)d

substitute for a and d

and then the required values for n

for eg.
n=101,
101st term t(101) = 2 + (101-1)*2 =202

Answer 8

101th no. is 202. see 1st no. was 2 i.e 1multiplied by 2
2nd was 4 i.e 2 multiplied by 2.therefore nth term will be 2 times n.

Answer 9

no thank you