Posts Tagged ‘arithmetic sequences’

Problem 738

Find the sum of the first 25 terms of the arithmetic series: -5, -4, -3, -2, -1, …

 

Solution:-

 

Find an by using the explicit formula for arithmetic sequences:

an = a1 + (n-1)d.

a1 = -5

a25 = 19

The use the formula for the sum of an arithmetic series:

Sn = \frac{n}{2}(a1 + an)

175

 

Problem 736

Find the 100th term of the sequence: -4, -2, 0, 2, ….

 

Solution:-

 

Find the common difference and use the explicit formula for arithmetic sequences:  .

an = a1 + (n-1)d.

a1  = -2

n = 100

d = 2

194

 

problem 685

 

Find the tenth term of the sequence: 1, 9, 17, 25, ….

 

Solution:-

 

Find the common difference and use the explicit formula for arithmetic sequences:

an =  a1 + (n – 1)d

a1 = 1 and d = 8

the tenth term = 73.