quiz study 2
q2 arithmetic series: Find the sum of the first 4040 terms of the arithmetic series2+5+8+11+...2+5+8+11+... .
1. Use the squence formula to find the 40th term First find the 40th term: a40=a1+(n−1)d =2+39(3) =119 2. Then find S(n) Sn = n(a1+an)/2 = 40 (2 + 119)/2 =2420
Geometric sequence
A geometric sequence is a sequence of numbers in which the ratio between any two consecutive terms is a constant. example: 1,3,9,27,81,... To find the formula for this geometric sequence, start by determining the common ratio, which is 3, since the terms are increasing by a factor of 3.
Arithmetic series: Finite arithmetic sequence
Finite arithmetic sequence: 5,10,15,20,25,...,200 Related finite arithmetic series: 5+10+15+20+25+...+200 Written in sigma notation:
Geometric series definition
a geometric series is the sum of an infinite number of terms that have a constant ratio between successive terms.
Arithmetic series: Infinite arithmetic sequence
Infinite arithmetic sequence: 3,7,11,15,19,... Related infinite arithmetic series: 3+7+11+15+19+...
q1 arithmetic series: Find the sum of the first 20 terms of the arithmetic series if a1=5 and a20=62
S20=20(5+62)/2 =670 n = 20 a1 = 5 an (this is the last term) = 62
Geometric series formula
Sn=a1(1-r^n)/1-r
q2: Finding Missing Numbers in Arithmetic Sequences What numbers are missing from the following arithmetic sequence? -3, 1, _____, 9, 13, _____
Step 1:The numbers -3 and 1 in the sequence are consecutive terms, because 1 comes directly after -3. The numbers 9 and 13 are also consecutive terms for the same reason. We can use these pairs of consecutive terms to find our common difference by subtracting -3 from 1 and subtracting 9 from 13. 1 - (-3) = 4 13 - 9 = 4 The common difference of this arithmetic sequence is 4. Our final sequence is -3, 1, 5, 9, 13, 17. Since our common difference is 4, we can check our answers by adding 4 to each term in this sequence and verifying that we get the next term in the sequence. -3 + 4 = 1 1 + 4 = 5 5 + 4 = 9 9 + 4 = 13 13 + 4 = 17 When we add our common difference of 4 to each term in the sequence, we end up with the next term in the sequence. This means that our answers are correct, so our missing numbers in the arithmetic sequence are 5 and 17.
q1: write a rule for the sequence 7, 12, 17, 22, 27, . . .
The common difference (d) is 5 and the first term (a) is 7. The nth term is given by the arithmetic sequence formula, so all you have to do is plug in the numbers and simplify: an=a1+d(n−1) an=7+5(n−1) an=7+5n−5 =2+5n
q1 continued: Find the 100th term in this sequence a(100)
a1 = 7, d = 5, solve for an an=a1+d(n−1) an=7+5(100−1)= an=502
Formula for geometric sequence
a1 = first number r= common ratio n = number in sequence
arithmetic sequence
an ordered set of numbers that have a common difference between each consecutive term. For example in the arithmetic sequence 3, 9, 15, 21, 27, the common difference is 6
q1 continued: find what number term in the sequence 377 is
an=a1+d(n−1) 1. need to solve for n where an = 377 2. 377 = 7 + 5(n-1) 3. n =75
q3 arithmetic series: Find the sum of an arithmetic series
problem is in screenshot:
q3 answer
use info to find d and then the arithmetic mean to find missing values
