An algebra problem by osman mohamad

Using ; $\frac { n(n+1) }{ 2 }$

We get: $n=50\\ S=\frac { n(n+1) }{ 2 } \\ S=\frac { 50\quad *\quad 51 }{ 2 } \\ S\quad =\quad \frac { 2550 }{ 2 } \\ S\quad =\quad 1275$

1+50 =51 also 2+49 =51 also 3 +48 =51 go by the same way until you reach 25 +26=51 Now you have 51 (25 times) 51 *25 =1275

We have , $S= 1+2+3+ ...... 50 \rightarrow (i)$

If we reverse the terms in the series the sum $S$ will still remain the same, $S = 50+49 +48 +...1 \rightarrow (ii)$

$(i)+(ii)$ , $2S = 51+51+.....+51 (50 times)$

which is, $2S = 50 \times 51$ $\Rightarrow S = \frac{50\times 51}{2} \Rightarrow \boxed{1275}$

Let us multiply the whole equation by 2 and add them together. We get 1+2+3.... added to 50+49+48.... and so on. Now, we have 51+51+51..., in total 51 multiplied by 50, which equals to 2550. Yet, since we have multiplied the equation by 2, we divide the answer by 2 also, giving us 1275.

sum of the 1st 'N' natural number=1+2+3.........+n(n+1)/2 we get n=50 =50(50+1)/2 =50(25.5) ans =1275

We sure can solve it using n (n+1)/2 - which gives us 50*51/2 = 1275 On the other side i've got something pretty interesting- A pattern. Many of you might know this before, but I'm putting this up for those who dont know. You get a pattern when you add the digits like: 1-10 = 55,
11-20= 155,
21-30= 255,
31-40= 355,
41- 50 = 455, etc...

This goes on as a pattern .. everytime a 100 increses.

we can solve by using arithmetic progression tn=a+(n-1)*d where tn=50;d=1;a=1 then substitute the value of n in sn=n/2(a+l)

1+50=51x25=1275

we have, s=n/2(2a+(n-1)d) here n=no.of terms .in an arithematic series=50 a=first term=1 d=common difference=1 substitute this in the above equation we get the answer. this is only applicable for arithematic progression.

By using arthematic progression ...u can solve it .. S=n/2(2a+(n-1)d)

There are 50 numbers, which increment by 1 each time, and start at 1 and end at 50, so the average of the 50 numbers would be (1+50)/2=25.5, and 25.5 50=255 5=1275

{n(n+1)}/2 .. here n=50............. so {50(50+1)}/2 =1275

50*(50/2)+(50/2)= 1275

50+1=51 49+2=51 ... 50 numbers divided by 2 equals 25. When you match them up like previously shown to get 51, you multiply that by 25 to get 1275!!

50 [50+1] /2=1275. n [n+1 ] /2 & solve.