Discover answers to your most pressing questions at Westonci.ca, the ultimate Q&A platform that connects you with expert solutions. Ask your questions and receive accurate answers from professionals with extensive experience in various fields on our platform. Explore comprehensive solutions to your questions from a wide range of professionals on our user-friendly platform.
Sagot :
The sum of the first 75 terms of the arithmetic sequence that has 10th term as 16 and the 35th term as 66 is 5400.
How to find the sum of terms using Arithmetic sequence formula
aₙ = a + (n - 1)d
where
- a = first term
- d = common difference
- n = number of terms
Therefore, let's find a and d
a₁₀ = a + (10 - 1)d
a₃₅ = a + (35 - 1)d
Hence,
16 = a + 9d
66 = a + 34d
25d = 50
d = 50 / 25
d = 2
16 - 9(2) = a
a = 16 - 18
a = -2
Therefore, let's find the sum of 75 terms of the arithmetic sequence
Sₙ = n / 2 (2a + (n - 1)d)
S₇₅ = 75 / 2 (2(-2) + (75 - 1)2)
S₇₅ = 37.5 (-4 + 148)
S₇₅ = 37.5(144)
S₇₅ = 5400
learn more on arithmetic sequence here: https://brainly.com/question/1687271
Thank you for trusting us with your questions. We're here to help you find accurate answers quickly and efficiently. Thank you for your visit. We're committed to providing you with the best information available. Return anytime for more. We're dedicated to helping you find the answers you need at Westonci.ca. Don't hesitate to return for more.