Question

how many terms of the ap:20,19 1/2,18 2/3' be taken so their sum is 300​

Answer 1

Answer:

The given AP is 20, 19 1/3, 18 2/3, ......... Here,  a = 20 and d = 19 1/3 -20 = 58/3 -20 = 58-60/3 = -2/3

Let the required number of terms be n.

Step-by-step explanation:

Here, a=20andd=(583−20)=−23. Let Sn=300. Then

n2×[2a+(n−1)d]=300⇒n2×[40+(n−1)×x(−23)]=300

n2.(122−2n)3=300⇒n(61−n)=900⇒n2−61n+900=0

⇒n2−36n−25n+900=0⇒n(n−36)−25(n−36)=0⇒(n−25)(n−36)=0

S25=300andS36=300

Sum of all terms from 26th to 36th is zero.