1.

What is the sum of the first 11 terms of an arithmetic progression if the 4th term is 11 and the 7th term is -4?1). -752). 553). 114). 100

Answer»

If the first term and the common DIFFERENCE of an arithmetic progression are ‘a’ and ‘d’ respectively, then, nth term of AP = a + (n - 1)d

Now,

4th term = a + 3d = 11----(1)

7th term = a + 6d = -4----(2)

Subtracting (1) from (2),

⇒ 6d - 3d = -4 - 11

⇒ 3d = -15

⇒ d = -15/3 = -5

Substituting in (1),

⇒ a = 11 - 3(-5) = 11 + 15 = 26

? Sum of n terms of AP = n/2 [2A + (n - 1)d]

∴ Sum of 11 terms = (11/2) × [2(26) + (11 - 1)(-5)] = (11/2) × (52 - 50) = 11/2 × 2 = 11


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