Posts Tagged ‘arithmetic series’

Problem 737

Find the sum of the first five terms of the arithmetic series:

an = 2n +2.

 

Solution:-

 

Find a1 and  a5  and use the formula for the sum of an arithmetic series:    Sn = \frac{n}{2} (a1 + an)

a1 = 2* 1 + 2 = 4

a5 =2*5 +2 = 12

Sn = 40

 

Problem 687

Find the sum of the first five terms of the arithmetic series: an =4n +7

 

Solution:-

 

Find  a1  and  an  by using the explicit formula for arithmetic

sequence: an = a1 + (n-1)d. The use the formula for the sum of an arithmetic series:

Sn  = \frac{n}{2}(a1 +an).

a1 =  4*1 +7 =11

a2 = 4*2+ 7 = 15

a3 = 4*3 + 7 = 19

a5 = 4*5  +7 = 27

d = 4

Sn  =  \frac{n}{2}(a1 +an).

=\frac{5}{2}(11+27)

=95

 

Problem 588

 

Find S20 for the arithmetic series 8 + 16 + 24 + 32 +…

 

Solution:-

 

a1 = 8, d =8

S20 = n/2[2*a1 + (n-1)*d]

S20 = 20/2[2*8 + (20-1)*8]

S20 = 1680