Math, asked by rviacastro5899, 9 months ago

How many terms with should be added in the series 1+5+9+13.....to get 190

Answers

Answered by abhi569
5

Answer:

10

Step-by-step explanation:

Given terms are in AP. This means they have a common difference.

Sum of first n terms of AP = (n/2)[ 2a + ( n - 1 )d ], where a is the first term and d is the common difference.

Here,

a = first term = 1

d = co. di. = 5 - 1 = 4  

 Let 190 be the nth term so

⇒ 190 = (n/2)[ 2(1) + ( n - 1 )4 ]

⇒ 380 = n( 2 - 4 + 4n )

⇒ 380 = ( 4n - 2 )n

⇒ 190 = 2n^2 - n

⇒ 2n^2 - n - 190 = 0

⇒ 2n^2 - 20n + 19n - 190 = 0

= > ( n - 10 )( 2n + 19 ) = 0

= > n = 10


Anonymous: Great
abhi569: :-)
Answered by anshikaverma29
2

Series : 1 + 5 + 9 + 13 + ......

a = 1

d = 5 - 1 = 4

Sₙ = 190

n = ?

Sₙ = n/2 [ 2a + (n - 1) d ]

190 = n/2 [ 2 + (n - 1) 4 ]

380 = n [ 2 + 4n - 4 ]

380 = n [ 4n - 2 ]

4n² - 2n - 380 = 0

2n² - n - 190 = 0

2n² - 20n + 19n - 190 = 0

2n( n - 10 ) + 19 ( n - 10 ) = 0

( n - 10 ) ( 2n + 19 ) = 0

n - 10 = 0 or 2n + 19 = 0

n= 10 , n = -19/2

But n can not be in fraction nor negative.

n = 10

Hence, 10 terms are required for a sum of 190.

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