Question

if the Sum of the first 9th term
on A. p. is equal to the sum of
its first 11th term find the Sum of its find 20th term​

Answer 1

GIVEN :-

• Sum of first 9 terms of an AP is equal to the sum of first 11 terms.

TO FIND :-

• Sum of first 20 terms.

SOLUTION :-

★ S(n) = n/2 [ 2a + (n-1)d ]

Here ,

• S(n) → sum of n terms.
• n → total number of terms.
• a → First term.
• d → Common difference.

According to question , sum of first 9 terms is equal to sum of first 11 terms.

➞ S(9) = S(11)

➞ 9/2 [2a + (9-1)d ] = 11/2 [2a + (11-1)d ]

➞ 9/2 [ 2a + 8d ] = 11/2 [ 2a + 10d ]

➞ 18a + 72d = 22a + 110d

➞ -4a - 38d = 0

➞ 2a + 19d = 0ㅤㅤㅤㅤ-------(i)

Now ,

We will find sum of 20 terms.

➞ S(20) = n/2 [2a+(20-1)d]

➞ S(20) = n/2 [2a+19d]

From eqⁿ (i) , 2a+19d = 0

➞ S(20) = n/2[0]

➞ S(20) = 0

Hence , sum of first 20 terms is 0.