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shutvik [7]
3 years ago
8

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

mmon difference d.
Mathematics
1 answer:
mina [271]3 years ago
6 0

Answer:

d = - \frac{5}{3}

Step-by-step explanation:

The sum to n terms of an arithmetic series is

S_n} = \frac{n}{2} [ 2a₁ + (n - 1)d ]

where a₁ is the first term and d the common difference

Here a₁ = 160, n = 25 and S_{25} = 3500 , thus

\frac{25}{2} [ (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 = - \frac{40}{24}  = - \frac{5}{3}

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See the attached image for a visual reference

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