Question

how many term of the series 1 + 5 + 9 + and so on must be taken so that their sum is 190?​

Answer 1

Answer:10 site d=4and sum=190

Answer 2

10 terms of series will give a sum of 190.

Step-by-step explanation:

We are given the following in the question:

Series:

1 + 5 + 9 +...

The series is an arithmetic progression with first term, a = 1 and common difference, d = 4.

The sum of n terms of an arithmetic progression is given by

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

Putting values, we get,

$S_n = \dfrac{n}{2}(2(1) + (n-1)(4))\\\\380 = n(2 + 4n-4)\\380 = 4n^2 - 2n\\4n^2-2n--380 = 0\\2n^2-n-190=0\\\text{From quadratic formula:}\\n = 10, n = \dfrac{-19}{2}$

Since n cannot be negative, we take n = 10.

Thus, 10 terms of series will give a sum of 190.

#LearnMore

How many terms of the series -9,-6,-3......must be taken so that the sum of them is 66

https://brainly.in/question/13307223