Question

find the sum of all the non negative terms of the following sequence 100,97,94.....

and the answer should be 1717

Answer 1

here is your solution.

Answer 2

Answer:

The correct answer is 1717

Given problem:

find the sum of all the non negative terms of the following sequence 100,97,94.....

Step-by-step explanation:

Given number sequence is 100, 97, 94  ...  [ which is in AP ]

here first term a = 100 and

common difference d = t₂ - t₁ = 97 - 100 = -3

here we need to find sum non- negative terms of the sequence

Let t$_{n}$ be the first negative term

t$_{n}$  = a + (n-1)d  ≤ 0

        100 + (n-1)(-3) ≤ 0

        100 - 3n +3 ≤ 0    

        103 - 3n ≤ 0  

        103 ≤  3n

         $\frac{103}{3} \leq n$  

        34.4 ≤  n      

from this we can conclude that if n is greater than 34  then the term will be negative

⇒ number of non negative terms = 34

The formula for sum of n terms in an AP = $\frac{n}{2} [ 2a + (n-1)d ]$  

⇒  sum 34 terms in AP =  $\frac{34}{2} [ 2(100) + (34-1)(-3) ]$  

                                      = $17 [ 200) + (33)(-3) ]$

                                      = $17 [ 200 -99 ]$

                                      = $17 [ 101 ]$

                                      = 1717