Final Math Unit, HELP!?

Question

Use the arithmetic sequence of numbers 1, 3, 5, 7, 9,…to find the following:
a) What is d, the difference between any 2 terms?


b) Using the formula for the nth term of an arithmetic sequence, what is 101st term?


c) Using the formula for the sum of an arithmetic sequence, what is the sum of the first 20 terms?



d) Using the formula for the sum of an arithmetic sequence, what is the sum of the first 30 terms?


e) What observation can you make about these sums of this sequence (HINT: It would be beneficial to find a few more sums like the sum of the first 2, then the first 3, etc.)? Express your observations as a general formula in "n."

Answer 1

The difference is 2
a_n= a_1 +(n-1)*r so a_a0a = 1+100*2 =201 You should have the formulas.Use them

Answer 2

1) d is the common difference between consecutive terms of AP. Thus, d=3-1=2 ans


2) nth term=a+(n-1)d
where a is first term of AP
n is term number
d is common difference
here a=1
n=101
d=2
thus 101st term=1+(101-1)2
=201ans

3)sum of n terms= n/2(a+l)
where l is last term of AP
here last term is 20th term
20th term= 1+(20-1)2
=39
thus sum=20/2(1+39)
10x40=400ans

4)similar to (3)
30th term=1+(30-1)2
=59
thus sum=30/2(59+1)
=15x60
=900ans

5) n/2[2a-(n-1)d]