Mr. 'U' knows it

Computer Science Level pending

22, 35, 48, 61, 74, 87, 100, 113, … \text{22, 35, 48, 61, 74, 87, 100, 113,} \dots

Above is a recursive sequence such that T 0 = 22 T_0=22 and T 1 = 35 T_1=35 . But the general term T n T_n for n ≥ 2 n \ge 2 is not known. Your task is to find the general term by observing the sequence. What is T 20 − T 16 T_{20}-T_{16} ?


The answer is 52.

Zeeshan Ali by Zeeshan Ali , 25, Pakistan

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2 solutions

Its an arithmetic progression with first term a=22 and the second being 35 which gives the common difference as 13(by subtracting the two as terms of an AP have general form of a+(n-1)d ) Now for finding T 20 T_{20} - T 16 T_{16} = [a+(20-1)d] - [a+(16-1)d] which leaves us with 4d (where d=13) hence the answer to the expression is 52

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It's an arithmetic progression with first term T 0 = 22 T_{0} = 22 and difference 13 , so T 20 − T 16 = ( 22 + 13 ⋅ 20 ) − ( 22 + 13 ⋅ 16 ) = 13 ⋅ 4 = 52 T_{20} - T_{16} = (22 + 13 \cdot 20) - (22 + 13 \cdot 16) = 13 \cdot 4 = 52

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