Question

52
12
+
32
a2
(S =
..... to n terms
a
a3 +
1
+
11
+-
1
2
+​

Answer 1

Answer:

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Sum of the First n Terms of an Arithmetic Progression

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We will learn how to find the sum of first n terms of an Arithmetic Progression.

Prove that the sum Sn of n terms of an Arithmetic Progress (A.P.) whose first term ‘a’ and common difference ‘d’ is

S = n2[2a + (n - 1)d]

Or, S = n2[a + l], where l = last term = a + (n - 1)d

Proof:

Suppose, a1, a2, a3, ……….. be an Arithmetic Progression whose first term is a and common difference is d.

Then,

a1 = a

a2 = a + d

a3 = a + 2d

a4 = a + 3d

………..

………..

an = a + (n - 1)d

Now,

S = a1 + a2 + a3 + ………….. + an−1 + an

S = a + (a + d) + (a + 2d) + (a + 3d) + ……….. + {a + (n - 2)d} + {a + (n - 1)d} ……………….. (i)

By writing the terms of S in the reverse order, we get,