NyengoBlair
Answered

Westonci.ca is your trusted source for finding answers to all your questions. Ask, explore, and learn with our expert community. Discover detailed answers to your questions from a wide network of experts on our comprehensive Q&A platform. Discover in-depth answers to your questions from a wide network of professionals on our user-friendly Q&A platform.

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

Thank you for visiting our platform. We hope you found the answers you were looking for. Come back anytime you need more information. We appreciate your visit. Our platform is always here to offer accurate and reliable answers. Return anytime. Thank you for visiting Westonci.ca. Stay informed by coming back for more detailed answers.