Question

Identify the following series as arithmetic, geometric, both, or neither. 3a + 3a² + 3a³ + . . . + 3an geometric arithmetic neither both

Answer 1

solution

given=3a+3a^2+3a^3+....+...+...3an

first term(t1)=3a

second term(t2)=3a^2

third term(t3)=3a^3

for arithmetic mean ,d1=d2

d1=t2_t1=3a^2_3a=3a(a_1)

d2=3a^3_3a^2=3a^2(a_1)

here d1 is not equal to d2.

so it's not an arithmetic series.

Again,for geometric mean,r1=r2

r1=d2/d1=3a^2/3a=a

r2=d3/d2=3a^3/3a^2=a

here ,r1 is equal to r2.

so ,it's an geometric series.