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Find the value of the series
1+4+2+8+3+12+4+16 +...+24+96+25+100

 May 18, 2023
 #1
avatar+274 
+1

Hello! Let me know if you have any questions about my explanation and if you find any typos or math mistakes.

The answer to your question is 1625.

 

The pattern may look complicated at first so lets break things down; break this series into two series. This will be: 1+2+3+4+...+24+25 and 4+8+12+16+...+96+100. What do you notice about these patterns? Well, the first pattern is consecutive integers from 1 to 25 (inlcusive) and the second pattern are all the multiples of 4 from 4 to 100 (inclusive).

 

Now let's find the value of both the series. First let's sum the numbers from 1 to 25 inclusive; this should be straight foward. So 1+2+3+4+...+24+25 = 325 and for our second series: 4+8+12+16+...+96+100 = 1300. And when you add 325+1300, you get 1625 as our final answer.

 

Here's some explanation on how I added the two smaller series (Source: https://brainly.in/question/12430191#:~:text=Answer,-10%20people%20found&text=The%20final%20answer%20is%2020200.): 

 

sum = (n/2)(a+b)

n = number of multiples

a = value of first multiple

b = value of last multiple

 May 18, 2023
 #2
avatar+214 
0

Good solution. Here's a quicker way. Once we separate the sequences, notice that 4(1+2+3+...+24+25) = 4(1)+4(2)+4(3)+...+4(24)+4(25)=4+8+12+...+96+199. So the second sequence is 4 times the first. So the answer is

5(1+2+3+4+...+23+24+25)=

5((25)(26))/2=

1625

 May 19, 2023

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