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the first term of an AP is 2,and the last term is 59.if the sum of the first terms is 610,Find the common difference​

Sagot :

Answer:

d = 3

Step-by-step explanation:

The sum to n terms of an AP is

[tex]S_{n}[/tex] = [tex]\frac{n}{2}[/tex] ( a + l)

where a is the first term and l the last term

Here a = 2, l = 59 and sum = 610 , then

[tex]\frac{n}{2}[/tex] (2 + 59) = 610

[tex]\frac{n}{2}[/tex] × 61 = 610 ( divide both sides by 61 )

[tex]\frac{n}{2}[/tex] = 10 ( multiply both sides by 2 to clear the fraction )

n = 20

Then the sequence has 20 terms with a₂₀ = 59

The nth term of an AP is

[tex]a_{n}[/tex] = a + (n - 1)d

where d is the common difference , then

2 + 19d = 59 ( subtract 2 from both sides )

19d = 57 ( divide both sides by 19 )

d = 3

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