sequences and sereis

Question 1

arithemtic series

Answer 1

a + (n-1)d

Question 2

geometric

Answer 2

ar^n-1

Question 3

sum of arithmentic

Answer 3

n/2 ( a+l) OR n/2 ( 2a+ (n-1)d))

Question 4

sum of geometric

Answer 4

a (1-r^n) / 1-r

Question 5

sum to infinity

Answer 5

a/1-r

Question 6

formula for number of terms “n” in a sigma question

Answer 6

do “l” (last value) - “r-1” (FIRST VALUE )

Question 7

formula for sum of values in sigma notation for a specific range of values

Answer 7

split the one notation into TWO notations each with a starting value of 1

the lower value has 1 taken away from it before substracting it from the larger value to account for the inclusion of the actual lower value

eg of this ….

NOTICE: that the lower value ( on top of the sigma )has 1 taken away from it before getting its summation

Question 8

convergent series

Answer 8

modulus of “r” is smaller than 1

Question 9

dont forget to use this formula instread for arithemtic additions !

Answer 9

1/2n ((2a + (n-1)d ))

use this equation to figure something otu when you dont have the “last value2