hello there
I want to know each and every step in detail to solve this equation.
please reply quickly
n
/2[2a + (n - 1)d] = 1800
thanks,
Then, | n | [2a + (n - 1)d] = 1800 |
2 |
I am presuming that what is in the box above is:ok then,
actually i was solving
The sum of how may tersm of the series 6 + 12 + 18 + 24 + ... is 1800 ? this question which is an example of arthmetic progression
where
a = 6, d = 6 and Sn = 1800 then i came across this equation which i dident understand how to solve
so please explain me in detail....
Then,
n
[2a + (n - 1)d] = 1800
2
thanks and regards
I am presuming that what is in the box above is:
\(\displaystyle \{n[2a + (n - 1)d]\}/2 = 1800?\) It helps to use grouping symbols and / for division
If I substitute in a = 6 = d and Sn = 1800
\(\displaystyle 1800 = \dfrac{n\{2*6 + 6(n-1)\}}{2} \implies\)
\(\displaystyle 1800 = \dfrac{6n(2 + n - 1)}{2} \implies\)
\(\displaystyle 1800 = 3n(n + 1) \implies \)
\(\displaystyle n(n + 1) = 600.\)
\(\displaystyle 6 + 12 + 18 +\ ...\ = 1800 \implies\)
\(\displaystyle 6(1 + 2 + 3 +\ ...) = 6(300) \implies\)
\(\displaystyle 1 + 2 + 3 +\ ...\ = 300 \implies \)
\(\displaystyle \dfrac{n(n + 1)}{2} = 300 \implies \)
\(\displaystyle n(n + 1) = 600\)