find the geometric series of a geometric sequence where a3=294 and common ratio of seven for a6 through a10.

Question

Did not let me put it as this

A3=a_3,

A6=a₆

A10=a₁₀

Answer 1

AN= 6(7)^(N-1)

A0 = 6

A1 =6(7)^0

A2= 6(7)^1

A3 = 6(7)^2 = 294

A4 = 6(7)^3= 2058

A5 = 6(7)^4

A6 = 6(7)^5 = 100,842 = about 100K=10% of a million

....

A7 = 6(7)^5 = 242,121,642 = about a quarter mill

multiply 6 by SN

S0 = 1

S1= 7+1 = 8

S2 =49+8 =57

S3 = 343 + 57 = 400 = (1-7^3)/(1-7) = 2400/6 = 400

S4 = (7)^0 + (7)^1 +(7)^2 + (7)^3 + (7)^4

S6 = (7)^0 + .....+ (7)^6= (1-7^7)/-6

S10 = (7)^0 + ....+ (7)^10 = (1-7^11)/-6

SN = (1-(7)^N+1 divided by 1-7 where 7 is the common ratio

series of sequence

N=3 is 2400

N=6 is 6 times (1-7^(7))/-6

N=10 is 6 times (1-7^11)/-6