By what amount should the first term increase so that the 31st term of

1.	By what amount should the first term increase so that the 31st term of an AP remains the same even if the common difference decreases by 9?1. 2702. 2903. 2504. 300
Answer» Correct Answer - Option 1 : 270 Given: The 31st term of an AP remains the same even if the common difference decreases by 9. Formula Used: n-th term of an AP = a + (n - 1)d, where a is the first term, n is the total number of terms and d is the common difference. Calculation: Let the initial first term be a₁ and the required first term be a₂. Let d be the common difference. Now, a₁ + 30d = a₂ + {30 × (d - 9)} ⇒ a₁+ 30d = a₂ + 30d – 270 ⇒ a₁ = a₂ – 270 ∴ The first term will be increased by 270.

By what amount should the first term increase so that the 31st term of an AP remains the same even if the common difference decreases by 9?1. 2702. 2903. 2504. 300

Answer» Correct Answer - Option 1 : 270

Given:

The 31st term of an AP remains the same even if the common difference decreases by 9.

Formula Used:

n-th term of an AP = a + (n - 1)d, where a is the first term, n is the total number of terms and d is the common difference.

Calculation:

Let the initial first term be a₁ and the required first term be a₂.

Let d be the common difference.

Now, a₁ + 30d = a₂ + {30 × (d - 9)}

⇒ a₁+ 30d = a₂ + 30d – 270

⇒ a₁ = a₂ – 270

∴ The first term will be increased by 270.