The sequence an = a + (n − 1)d

Question

The sequence a_n = a + (n − 1)d

 is an arithmetic sequence in which a is the first term and d is the  ---Select--- common sum partial difference partial sum common difference . So for the arithmetic sequence a_n = 8 + 7(n −1)

 the first term is  , and the common difference is  

Answer 1

common difference = d = 7

first term = a = 8

a1 = 8

a2 = 8+7(2-1) = 15

a3= 8+ 7(3-1) = 22

a4 = 8+ 7(4-1) = 29

a5 = 8+ 7(5-1) = 36

a6 = 8+ 7(6-1) = 43

an = 8 + 7(n-1)

a7 = 8 +7(7-1)= 8+7(6) = 8+42=50

a8 =8 +7(8-1)= 8+7(7) = 8+49= 57

for partial sums

a1 through a8 = 8,15, 22,29,36,43,50,57,64,71, 77

s1 = 8

s2 = 8+15= 23

s3 =23+22= 45

s4 = 45+29 = 74

s5 = 74+36= 110

s6 = 110+43 = 153

s7 = 153+50= 203

s8 = 203+57 = 260

sn= (n/2)(a1+an) an=8,15,22,29,36,43,50,57,64...

s1 =(1/2)(8+8)=8

s2 = (2/2)(8+15)= 22

s3 = (3/2)(8+22)=45

s4=(4/2)(8+29)= 2(37)=74

s5= (5/2)(8+36)=2.5(44= 110

s6 = 6/2(8+43) = 3(51) =153

s7 = 7/2(8+50) = 3.5(58) = 203

s8 = 8/2(8+57)= 4(65= 260

s8 = (8/2)(8+57) = 4(65)= 260

there is no constant common difference. the differences are 15,29,36,43,50,57,64, ...

common variable difference = 8+7(n-1)