Question

what is the sum of the first 10 terms of the sequence defined by an=2n-3
a.7
b.17
c.80
d.82

Answer 1

Answer: The sum of the first ten terms of the sequence is 80

Answer 2

As per arithmetic sequence, the sum of the first 10 terms of the sequence is 80.

What is  an arithmetic sequence?

"Arithmetic Progression is a sequence of numbers in order, in which the difference between any two consecutive numbers is a constant value."

Given, the sequence is

$a_{n} = 2n-3$

Therefore,

$a_{1} = 2(1)-3 = -1$

$a_{2} = 2(2)-3 = 1$

$a_{3} = 2(3)-3 = 3$

$a_{2}- a_{1} = 1 - (-1) = 2\\a_{3}- a_{2} = 3-1 = 2$

Therefore, it is clear that the given sequence is an arithmetic sequence.

Here, the first term(a) is - 1, common difference(d) is 2, and number of terms(n) is 10.

Therefore, the sum of the first 10 terms of the sequence is

$\frac{n}{2}[2a+(n-1)d]\\= \frac{10}{2}[2(-1)+(10-1)2]\\= 5[-2+(9)2]\\= 5[-2+18]\\= 5(16)\\= 80$

Learn more about an arithmetic sequence here: https://brainly.com/question/20385181

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