Question

If the first four terms of an arithmetic sequence are: a, 2a, b and a-6-b for some
numbers "a" and "b", then the value of the 100 term is :

Answer 1

Answer:

The value of the 100 term is - 100.

Step-by-step explanation:

Here we know that a, 2a, b and a-6-b are in arithmetic progression.

First find out the common difference,

• d = a₂ - a₁
• d = 2a - a
• d = a

• d = a₃ - a₂
• d = b - 2a

Substitute the value of d,

• a = b - 2a
• b = a + 2a
• b = 3a

Now,

• a₄ = a + 3d

We know, d = a

• a - 6 - b = a + 3a
• a - 6 - b = a + 3a
• a - 6 - b = 4a

Substituting the value of b,

• a - 6 - 3a = 4a
• - 6 = 4a + 3a - a
• - 6 = 4a + 2a
• - 6 = 6a
• a = -6/6
• a = - 1

Now, we know that d = a which is also equal to - 1.

• a₁₀₀ = a + 99d

Again d = a

• a₁₀₀ = a + 99a
• a₁₀₀ = 100a

Substituting the value of a,

• a₁₀₀ = 100 × - 1
• a₁₀₀ = - 100

∴ The value of the 100 term is - 100.

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