Question
Find the sum:
$(-5) + (-8) + (-11) + ..... + (-230).$
$(-5) + (-8) + (-11) + ..... + (-230).$
✓
Answer
Given,
A.P. $(-5) + (-8) + ..... (-230)$
Here,
First term $a = -5$
Difference $d = -8 - (-5) = -8 + 5 = -3$
and Last term $a_n= -230$
We know $a_n= a + (n - 1)d$
$⇒ -230 = -5 + (n - 1)(-3)$
$⇒ -230 = -5 - 3n + 3$
$⇒ -230 = -2 - 3n$
$⇒ -228 = -3n$
$\Rightarrow\ \text{n}=\frac{-228}{-3}=76$
We know, sum of n terms,
$\text{S}_\text{n}=\frac{\text{n}}{2}[2\text{a}+(\text{n}-1)\text{d}]$
$\Rightarrow\ \text{S}_{76}=\frac{76}{2}[2(-5)+(76-1)(-3)]$
$ \Rightarrow S_{76}=38[-10+75 \times-3] $
$ \Rightarrow S_{76}=38[-10-225] $
$ \Rightarrow S_{76}=38[-235] $
$ \Rightarrow S_{76}=-8930$
Hence, Sum of given A.P. is -8930.
A.P. $(-5) + (-8) + ..... (-230)$
Here,
First term $a = -5$
Difference $d = -8 - (-5) = -8 + 5 = -3$
and Last term $a_n= -230$
We know $a_n= a + (n - 1)d$
$⇒ -230 = -5 + (n - 1)(-3)$
$⇒ -230 = -5 - 3n + 3$
$⇒ -230 = -2 - 3n$
$⇒ -228 = -3n$
$\Rightarrow\ \text{n}=\frac{-228}{-3}=76$
We know, sum of n terms,
$\text{S}_\text{n}=\frac{\text{n}}{2}[2\text{a}+(\text{n}-1)\text{d}]$
$\Rightarrow\ \text{S}_{76}=\frac{76}{2}[2(-5)+(76-1)(-3)]$
$ \Rightarrow S_{76}=38[-10+75 \times-3] $
$ \Rightarrow S_{76}=38[-10-225] $
$ \Rightarrow S_{76}=38[-235] $
$ \Rightarrow S_{76}=-8930$
Hence, Sum of given A.P. is -8930.
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