The sum of the first 26 terms of an AP 1, 3, 5, 7, ... is -
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Given:
First term, a = 1
Common difference, d = a2 - a1 = 3 - 1 = 2
Number of terms, n = 26
Formula:
an = a + ( n - 1 )d
Sn = n/2 ( a + an )
To Find:
The sum of the first 26 terms.
Explanation:
We need to find what's the last term of the AP.
a26 = 1 + ( 26 - 1 )(2)
a26 = 1 + 25(2)
a26 = 1 + 50 = 51
The last term of the AP is 51.
Now, we need to find the sum of the first 26 terms.
S26 = 26/2 ( 1 + 51 )
S26 = 13 ( 52 )
S26 = 676
Answer:
The sum of the first 26 terms of the AP is 676 .
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