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Hi,

Given the first term and the common difference of an arithmetic sequence find the first five terms and explicit formula.

1.) a1 = 28, d=10

28,38,48,58,68

a(n) = a(1) + d(n - 1)

a(n) = 28 + 10(n - 1)

a(n) = 28 + 10n - 10

a(n) = 18 + 10n <==ANSWER

2.) a1= -38, d=-100

a(n) = a(1) + d(n - 1)

a(n) = -38 - 100(n - 1)

a(n) = -38 - 100n + 100

a(n) = 62 - 100n <==ANSWER

3.) a1= -34, d=-10

a(n) = a(1) + d(n - 1)

a(n) = -34 - 10(n - 1)

a(n) = -34 - 10n + 10

a(n) = -24 - 10n <==ANSWER

4.) a1 = 35, d=4

a(n) = a(1) + d(n - 1)

a(n) = 35 + 4(n - 1)

a(n) = 35 + 4n - 4

a(n) = 31 + 4n <==ANSWER

The next part says:

Given the first term and the common difference of an arithmetic sequence find the recursive formula and the three terms in the sequence after the last one given.

1.) a1 = 3/5, d= -1/3

a(n+1) = a(n) - 1/3 <==ANSWER

3/5, 4/15, -1/15, -2/5 <==ANSWER

2.) a1 = 39, d=-5

a(n + 1) = a(n) - 5 <==ANSWER

39, 34, 29, 24 <==ANSWER

I hope that helps!! :-)

Explicit Formula For Arithmetic Sequence

enable the unique series 3 numbers are a, a + 3, and a + 6. If the 1st huge sort is extra advantageous through a million, the 2nd extra advantageous through 6 , and the 0.33 through 19 So, the geometric series 3 numbers are a + a million, a + 9, and a + 25. Above numbers following geometric series so, t? / t? = t? / t? (a + 9)/(a + a million) = (a + 25)/(a + 9) circulate multiplication. (a + 9)(a + 9) = (a + 25)(a + a million) FOIL approach: the made from 2 binomials is the sum of the products of the 1st words, the Outer words, the interior words and the final words. a2 + 9a + 9a + eighty one = a2 + 1a + 25a + 25 a2 + 18a + eighty one = a2 + 26a + 25 Subtract a2 from the two element. 18a + eighty one = 26a + 25. Subtract 18a from the two element. eighty one = 8a + 25 Subtract 25 from the two element. 8a = fifty six Divide the two element through 8. a = 7. consequently the unique series is 7, 10, 13. The geometric series is 8, sixteen, 32.