an arithmetic series has first term 160 and common difference d . the sum of the first 25 terms of the series 3500 . find the common difference d.

d = -

Step-by-step explanation:

The sum to n terms of an arithmetic series is

= [ 2a₁ + (n - 1)d ]

where a₁ is the first term and d the common difference

Here a₁ = 160, n = 25 and = 3500 , thus

[ (2 × 160) + 24d ] = 3500, that is

12.5(320 + 24d) = 3500 ( divide both sides by 12.5 )

320 + 24d = 280 ( subtract 320 from both sides )

24d = - 40 ( divide both sides by 24 )

d = -  = -

none of the option is correct.

step-by-step explanation:

it says to find which expression equals 9^3 sqrt 10 = ?

9^3 sqrt 10 = 729 sqrt 10.

checking option a. 5 sqrt 10 + 4 sqrt 10

5 sqrt 10 + 4 sqrt 10

= 9 sqrt 10.

checking option b. 5^3 sqrt 10 + 4^3 sqrt 10

5^3 sqrt 10 + 4^3 sqrt 10

= 125 sqrt 10 + 64 sqrt 10

= 189 sqrt 10.

checking option c. 5 sqrt 10 + 4^3 sqrt 10

5 sqrt 10 + 4^3 sqrt 10

= 5 sqrt 10 + 64 sqrt 10

= 69 sqrt 10.

checking option d. 5^3 sqrt 10 + 4 sqrt 10

5^3 sqrt 10 + 4 sqrt 10

= 125 sqrt 10 + 4 sqrt 10

= 129 sqrt 10.

hence, none of the option is correct.