Question

Find the sum of the series given in sigma notation.

Answer 1

Answer:

Option b is correct 175

Step-by-step explanation:

n = 7

k = 6

3k -2 ------1

put k = 6 in above eq. for finding first term

  a1 = 3(6) - 2  = 18 - 2 = 16

put k = 7 in above eq. for finding first term

 a2 = 3(7) - 2 = 21 - 2 = 19

 a3 = 3 (8) - 2 = 24 - 2 = 22

16, 19 , 22, ...  //Arithmetic series formation

a1 = 16 , a2 = 19

d = a2 - a1 = 19 - 16 = 3 //Difference of first two terms

Using sum forumula for arithmetic series

sum = $\frac{n}{2}(2a1 + (n-1)d)$

      = $\frac{7}{2}(2a1 + (7-1)d)$

      = $\frac{7}{2}(2(16) + (6)3)$

      =  $\frac{7}{2}(32 + 18)$    

      =  $\frac{7}{2}(50)$

      = 7 * 25

      = 175