In an arithmetic sequence, the sum of the second and eighth terms is $5$, and the product of the fourth and fifth terms is also $5$. What is the sum of the first $20$ terms of this sequence?

Guest Sep 24, 2021

#1**0 **

5=F + D + F + 7D,

5=(F + 3D) * (F + 4D), solve for F, D

Use substitution to get:

F==1/2 - this is the first term

D==1/2 - this is the common difference

Your sequence looks like this:

0.5 , 1 , 1.5 , 2 , 2.5 , 3 , 3.5 , 4 , 4.5 , 5 , 5.5 , 6 , 6.5 , 7 , 7.5 , 8 , 8.5 , 9 , 9.5 , 10 , **>>Number of terms = 20>>Total Sum == 105**

Guest Sep 24, 2021