Question

For the following exercises, use the formula for the sum of the first n terms of each arithmetic sequence.

3.2 + 3.4 + 3.6 + … + 5.6

Answer 1

Consider the following arithmetic series:

3.2 + 3.4 + 3.6 + … + 5.6

 

Use the formula for the sum of first n terms of an arithmetic series,

Sn = n(a1 + an)/2 ...... (1)

 

In the above series, first term is a1 = 3.2

Last term is an = 5.6

 

Common difference of above arithmetic series is computed by subtracting first term from its second term. That is,

d = a2 – a1

    = 3.4 – 3.2

   = 0.2

 

Use the formula for the general term of an arithmetic sequence,

an = a1 + (n – 1)d ...... (2)

 

Substitute a1 = 3.2, an = 5.6 and d = 0.2 in formula (2) and find the value of n,

          5.6 = 3.2 + (n – 1) × 0.2

0.2(n – 1) = 2.4

       n – 1 = 2.4/0.2

       n – 1= 12

             n = 13

 

So, there are 13 terms in the above sequence.

Substitute a1 = 3.2, an = 5.6 and n = 13 in formula (1) and simplify,

S13 = 13(3.2 + 5.6)/2

       = 13 × 8.8/2

       = 57.2

 

Therefore, the sum of above arithmetic series is S13 = 57.2.

Therefore, the sum of above arithmetic series is S13 = 57.2.