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The sum of the first 25 terms of the arithmetic sequence 4,9,14,19,24...

Sagot :

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Answer:

THE SUM OF THE FIRST 25 TERMS OF THE ARITHMETIC SEQUENCE 4,9,14,19,24.....

ARITHMETIC SEQUENCE in mathematical term  is a set of numbers that are in order.  

example: 3, 5, 7, 9,..

this sequence has a difference of 2 between each number

where:

  • 3 is first term
  • 5 is second term
  • 7 is third term
  • 9 is 4th term

Term it is the number in the sequence.

Arithmetic Sequence  

Denote this partial sum by Sn, Then

Sn= a1 + (n-1) d,  

where n is the number of terms,  a1 is the first term and d is the difference of each number.

The sum of the first n terms of an arithmetic sequence is called an arithmetic series .  

First find the 25th term of arithmetic sequence 4, 9, 14, 19, 24.  

( ∑(k=0)^(n-1)( a+kd)=  n/2 ( 2a+(n-1)d

where the given is  

a= 4 ( the first term)

d= 5 ( the " Common difference"  between each number or term

n= 25 ( how many terms to add up )

Solution: ∑( 4 + k * 5) = 25/ 2 ( 2(4) + (25-1) 5

                                   = 25/2 ( 128)  

                                   = 12.5 ( 128)  

                                    = 1600

therefore the answer is 1600.

for another information  please open the link below

brainly.ph/question/825249

brainly.ph/question/132557

brainly.ph/question/324549