Consider the arithmetic series

Question

7+19+31+43+...+163.

calculate the sum of the series.? 

 

Answer 1

The arithmetic sequnce 7 + 19 + 31 + 43 + ......+ 163

Common difference d = t₂ -t₁  

In the above sequence d = 19 - 7 = 12.

a = 7

Sum of the sequence = n/2 [ a + l ]

Where a = first term and l = last term.

• Find the value of n.

Last term of the sequence = 163

n th term is an = a + (n - 1)d

163 = 7 + ( n - 1)12

163 = 7 + 12n - 12

163 = 12n - 5

163 + 5 = 12n

168 = 12n

n = 168/12

n = 14

Sum = 14/2 [ 7 + 163]

= 7(170)

= 1190

7 + 19 + 31 + 43 + ......+ 163 = 1190.