Question

How many terms of the arithmetic sequence 2 8 14 20 will give a sum of 660

Answer 1

Answer:

5 terms its answers mark as brianliat

Answer 2

First 15 terms of the arithmetic sequence 2 8 14 20 will give a sum of 660

Solution:

Given is a arithmetic progression

2 , 8 , 14 , 20

Then, given that,

sum of n terms = 660

The sum of n terms in arithmetic progression is:

$S_n = \frac{n}{2} ( 2a + (n-1)d )$

Where,

"d" is the common difference between terms

a is the first term of sequence

n is the number of terms

From given,

2 , 8 , 14 , 20

$a = 2 \\\\d = 8 - 2 = 6 \\\\S_n = 660$

Substituting the terms we get,

$660 = \frac{n}{2} ( 2 \times 2 + (n - 1) \times 6) \\\\660 = \frac{n}{2} ( 4 + 6n - 6) \\\\1320 = 4n + 6n^2 - 6n\\\\6n^2 - 2n - 1320 = 0\\\\Divide\ by\ 2\\\\3n^2 - n - 660 = 0$

$\left(3n+44\right)\left(n-15\right) = 0\\\\Thus,\\\\3n + 44 = 0\\\\3n = -44\\\\n = \frac{-44}{3} \\\\Also\\\\n - 15 = 0\\\\n = 15$

Ignore negative value

Thus, n = 15

Thus, sum of first 15 terms will give a sum of 660

Learn more:

How many terms of the arithmetic sequence 5,7,9,...,must be added to get 140

https://brainly.in/question/2837057

The second term of an arithmetic sequence is 7.the sum of the first four terms in the arithmetic sequence is 12.find the first term and the common difference of the sequence

https://brainly.in/question/5652390