Question

2. | 0/1 POINTS || PREVIOUS ANSWERS HARMATHAP12 6.1.043. 15 Find the sum of the first 110 terms of the arithmetic sequence 9, 9982.5

Answer 1

Answer:

Given arithmetic sequence :

$9, \frac{15}{2}, 6, . . .. . . .$

Sum of first 110 terms of the sequence = ?

As we know, the formula for calculating the sum of first "n" terms of an arithmetic sequence with first term "a" and common difference "d" is given as -

$Sum \ of \ first \ n \ terms, \ S_{n} = (2a+(n-1)d) \times \left ( \frac{n}{2} \right )$

Using the above formula, we can find the sum of first 110 terms for the given arithmetic sequence as -

First term, a = 9

Common difference, d = $\frac{15}{2} -9 = -\frac{3}{2}$

n = 110

$Sum \ of \ first \ 110 \ terms, \ S_{110} = (2(9)+(110-1)\left ( -\frac{3}{2} \right )) \times \left ( \frac{110}{2} \right )$

  $= (18+(109)\left ( -\frac{3}{2} \right )) \times \left ( \frac{110}{2} \right )$

  $= (18 -\frac{327}{2}) \times 55$

  $= -\frac{291}{2} \times 55$

  

Thus, the sum of the first 110 terms of the given arithmetic sequence is -8002.5 .