For all possible integers n satisfying 2.25 ≤ 2 + 2n+2 ≤ 202, the number of integer values of 3 + 3n+1 is
Explanation:
Given, 2.25 ≤ 2 + 2n+2 ≤ 202
⇒ 0.25 ≤ 2n+2 ≤ 200
Case 1: 0.25 ≤ 2n+2 ∴ n + 2 ≥ -2 ⇒ n ≥ -4
Case 2: 2n+2 ≤ 200 This is true when n ≤ 5
∴ -4 ≤ n ≤ 5
Now, 3 + 3n+1 should be an integer
This is possible when n = -1, 0, 1, 2, 3, 4 and 5
∴ n can take 7 values.
Hence, 7.
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