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Find the arithmetic series, find S25 !!! Show work please

Find the arithmetic series, find S25 !!! Show work please-example-1
User Rob Earlam
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1 Answer

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21)


a_(n) = a₁ + d(n - 1) ; where a₁ is the first term and d is the difference.

a₁ = 3, d = 4 →
a_(n) = 3 + 4(n - 1) = 3 + 4n - 4 = 4n - 1


a_(25) = 4(25) - 1 = 100 - 1 = 99


S_(n) =
(a_(1) +a_(n) )/(2)(n)


S_(25) =
(3 +99 )/(2)(25) =
(102 )/(2)  (25) = 51 · 25 = 1275

Answer:
a_(n) = 4n - 1 , 1275

23)


a_(n) = a₁ + d(n - 1) ; where a₁ is the first term and d is the difference.

a₁ = 4, d = 10 →
a_(n) = 4 + 10(n - 1) = 4 + 10n - 10 = 10n - 6


a_(25) = 10(25) - 6 = 250 - 6 = 244


S_(n) =
(a_(1) +a_(n) )/(2) (n)


S_(25) =
(4 +244 )/(2) (25) =
(248)/(2)(25) = 124 · 25 = 3100

Answer:
a_(n) = 10n - 6 , 3100

User Muhammedv
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