Find S11 for the arithmetic series -9,-1,7,15...

Answer 1

sum = number of terms times the average of 1st and last terms

a1 = -9

a2=-1

a3 =7

a4 = 15

a5 = 23

a6 =31

an = 8n-17

a11= 8(11)-17 = 88-17 =71

sn = n(a1+an)/2 = 11(-9+71)/2 =11(62)/2 = 11(31) = 362

s2=2(-9-1)/2=-10

s3 =3(-9+7)/2=-3

s11=11(-9 + 8(11)-17)/2 = (11/2)(88-26) = 11(62/2) =11(31) = 362

Answer 2

For arithmetic series,

a_n = a₁+d(n-1)

For this sequence, the difference, d, between numbers is 8.

a₁ = -9

a_n = -9 + 8(n-1)

a₁₁ = -9 + 8(10) = 71