Question

The sum of first 6 terms of AP is zero and forth term is 2. Find the sum of 20 terms of an AP

Answer 1

Solution:-

S6 = 0

=> 6/2 [ 2a + ( 6-1)d] = 0

=> 6 [ 2a + 5d] = 0

=> 2a + 5d = 0.__________(1)

& a4 = 2

=> a + 3d = 2___________(2)

From eq (1) & (2).

By Elimination Method. we get,

-d = -4

=> d = 4

putting d = 4 in eq (2). we get,

a = 2 - 12

=> a = -10.

Now,

S 20 = 20/2 [ 2a + ( n-1) d]

=> 10 [ -20 + 19 × 4]

=> 10 [ -20 × 76]

=> 10 × 56

=> 560.

Hence, The sum of First 20 term is 560.

Answer 2

The sum of first 6 terms is 0.

So the first 3 terms have corresponding negative values of the next 3 terms.

Means, the AP will be x, y, z, -z, -y, -x,......

This concept is very helpful to answer such questions.

Here, the 4th term is 2. so the 3rd term becomes -2.

So the common difference is 2 - (-2) = 4.

So the AP will be - 10, - 6, - 2, 2, 6, 10,......

a = - 10

d = 4

So let's find the sum of 20 terms.

n = 20

S_n = n/2 [2a + (n - 1)d]

S₂₀ = 20/2 [2 × -10 + 4(20 - 1)]

S₂₀ = 10 [-20 + 19 × 4]

S₂₀ = 10 [-20 + 76]

S₂₀ = 10 × 56

S₂₀ = 560

∴ 560 is the answer.

Thank you. Have a nice day. :-))

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