Math, asked by olioachlys01, 1 year ago

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

Answers

Answered by gouarv22394
7

Answer:

5 terms its answers mark as brianliat

Answered by sharonr
14

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

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