If your question mean:
3 ∙ (0.15) ∙ 4 + 3 ∙ ( 0.15) ∙ 5 +3 ∙ (0.15) ∙6 +⋯+ 3 ∙ (0.15) ∙ 11
then
3 ∙ (0.15) ∙ 4 + 3 ∙ ( 0.15) ∙ 5 +3 ∙ (0.15) ∙6 +⋯+ 3 ∙ (0.15) ∙ 11 =
3 ∙ 0.15 ∙ ( 4 + 5 + 6 + 7 + 8 + 9 + 10 + 11 ) =
0.45 ∙ ( 4 + 5 + 6 + 7 + 8 + 9 + 10 + 11 )
4 + 5 + 6 + 7 + 8 + 9 + 10 + 11 are members of arithmetic progression with initial member a1 = 4 and the common difference d = 1
You have 8 members in this progression.
Sum of the n members in A.P:
S = n ( a1 + an ) / 2
In this case:
n = 8 , a1 = 4 , an = 11
S = 8 ( 4 + 11 ) / 2 = 8 ∙ 15 / 2 = 120 / 2 = 60
3 ∙ (0.15) ∙ 4 + 3 ∙ ( 0.15) ∙ 5 +3 ∙ (0.15) ∙6 +⋯+ 3 ∙ (0.15) ∙ 11 =
0.45 ∙ ( 4 + 5 + 6 + 7 + 8 + 9 + 10 + 11 ) =
0.45 ∙ 60 = 27
3(0.15)4+3(0.15)5+3(0.15)6+⋯+3(0.15)11
2 answers
I assume you meant
3(0.15)^4+3(0.15)^5+3(0.15)^6+⋯+3(0.15)^11
Given a GP with
a =3
r = 0.15
You have terms 5-12 of the geometric series. That is just
S12 - S4
Since Sn = a(1-r^n)/(1-r), that gives you
= 3(1 - 0.15^12)/(1 - 0.15) - 3(1 - 0.15^4)/(1 - 0.15) = 0.00178676
3(0.15)^4+3(0.15)^5+3(0.15)^6+⋯+3(0.15)^11
Given a GP with
a =3
r = 0.15
You have terms 5-12 of the geometric series. That is just
S12 - S4
Since Sn = a(1-r^n)/(1-r), that gives you
= 3(1 - 0.15^12)/(1 - 0.15) - 3(1 - 0.15^4)/(1 - 0.15) = 0.00178676