Question

Pz solve it fast
Its urgent.........​

Answer 1

`\larg\boxed{\large\boxed{57}}`

Step-by-step explanation:

1. Write the general general form of the nth term of a geometric series

`a_n=a_1* r^(n-1);n=1,2,3,...`

`r=\text{common ratio}`

`a_1=\text{first term}`

2. Write the expression for the product of the first five terms equal to 243

`a_1* a_2* a_3* a_4* a_5=243\\\\a_1* (a_1* r)* (a_1* r^2)* (a_1* r^3)* (a_1* r^4)=243`

`a_(1)^5r^(10)=243`

`(a_(1)r^(2))^5=3^5`

`a_1r^2=3`

3. Write the third term

Notice that the third term is
`a_1* r^2`

Then, the third term is 3.

4. Goe with the aritmetic series: the tenth term is 3

`a_(10)=3`

5. Write the expression for the sum of the first 19 terms of the arithmetic series

General formula:

`S = (n/2)* \bigg(2a_1+(n-1)d\bigg)`

For n = 19

`S = (19/2)* (2a_1+18d)`

6. Write the expression for the term #10

`a_(10)=a_1+9d=3\\\\2(a_1+9d)=2(3)\\\\2a_1+18d=6`

7. Substitute in the expression for S

`S=(19/2)* 6\\\\S=57\leftarrow answer`