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 = -  = -

first, we define the variables:

x: number of years after 1950

f (x): amount of vinyl sold.

then, with the variables defined, we have:

68594 vinyl records were sold in 1958 > f (8) = 68594

91299 vinyl records were sold in 1961 > f (11) = 91299

38720 vinyl records were sold in 1952 > f (2) = 38720

161743 vinyl records were sold in 1967 > f (17) = 161743

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step-by-step explanation: