CBSEi Class 10 Sequences (AP and GP) CORE

Thus, the sum of first n terms of an AP is given by
Sn = [2a + (n 1) d]
Note that
last term of the AP = = a+(n 1) d.
Let = a + (n 1) d.
So, , = [2a + (n 1) d]
= [a + a + (n 1) d]
= [a + ]
Hence = [a+ ],
where is the last term or nth term.
The above method is similar to the one used by the great German mathematician Carl
friedrich Gauss (1777-1855) when he was in elementary school. His teacher asked the
class to find the sum of first 100 natural numbers. Gauss found the sum as follows:
1 + 2 + 3 + 4 + ………… + 98 + 99 + 100
100 + 99 + 98 + 97 + ……….... + 3 + 2 + 1
101 + 101 + 101 + 101 + ………… + 101 + 101 + 101
101, 100 times
i.e., sum = = 5050
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