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(a) Complete this table.
[Table_1]
(b) Explain how you know that $T_6 = 681$ without using the method in the table.
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(c) When a T is placed at the end of a line, it still has a T-value. The T "wraps round" like this.
Work out $T_9$.
$T_9 =$ ..........................................................................................
530
553
531
(a) Work out the greatest T-value for a T that fits completely on this grid.
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(b) Complete this statement for the numbers in the grid.
In each row the numbers increase by 1 and in each column the numbers increase by ................... .
(c) Complete the squares in this T using expressions in terms of $n$.
(d) Complete this working to show that $T_n = 40n + 441$.
The first line of working has been started for you.
$T_n = (n + ............)^2 - n (n + ............)$
(e) When $T_n = 2641$, find the value of $n$.
$n = .........................................................$
(f) Explain why 840 cannot be a T-value.
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578
509
527
The T is now placed on a new grid that is 11 squares wide.
$T_1, T_2, T_3, T_4, T_5, \ldots$ form a sequence.
(a) Complete this table.
[Table_1]
Shape number $n$ | 1 | 2 | 3 | 4 | 5 | $|$ | 8]
T-value $T_n$ | 573 | 661 | 705 | | | $|$ | ]
(b) (i) Find a formula, in terms of $n$, for $T_n$.
$T_n =$ ext{.....................................}
(ii) Show that your formula in part b(i) gives the correct result for $T_{10}$.
587
547
593
A different T is placed on a grid that is $w$ squares wide. The T has a horizontal bar of length 3 and a vertical bar of length 3.
Complete the squares in this T using expressions in terms of $n$ and $w$.
511
500
512
