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. 270
2. 290
3. 250
4. 300
1. 270
2. 290
3. 250
4. 300
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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.