Fifth term of an arithmetic sequence is 11 . What is the sum of first 9 terms of this sequence ?
Answers
Given : 5th term of an arithmetic sequence is 11
To find : sum of first 9 terms
Solution :
An arithmetic sequence is a sequence of numbers in which common difference between two consecutive terms is always equal.
We are given that 5th term is 11.
=> a5 = 11
We know that,
- an = a + (n - 1) d
So, we get :
=> a5 = a + 4d = 11
=> a + 4d = 11
Multiply both sides with 2
=> 2 ( a + 4d ) = 11 (2)
=> 2a + 8d = 22 . . . (1.)
Now we have formula for sum of AP,
- Sn = n / 2 [ 2a + ( n - 1 ) d ]
For n = 9
=> S9 = 9 / 2 [ 2a + 8 d ]
Now substitute value of [ 2 a + 8d ] from equation (1)
=> S9 = 9 / 2 [ 22 ]
=> S9 = 9 × 11
=> S9 = 99
Hence the sum of first 9 terms of the given sequence is 99.
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