7. An ironmonger makes gates from metal rods bolted together. Each rod is 0·5 m long. Bolt
Rod 0·5 m Length = 0·5 m
(a) Draw a gate of length 2 m. (b) Copy and complete the table below: Length l (m)
Number of rods n Number of bolts N
(c) Write down a formula connecting N and l. (d) Write down a formula relating n and l. (e) Find a formula connecting N and n. (f) How many rods are needed to make a fence of length 22·5 m? (g) How many bolts are needed to make a fence of length 13 m? (h) How many bolts are needed to make a fence containing 314 rods?
8. The sum of the fi rst n terms of an arithmetic sequence is given by Sn = n 2 − 12n. (a) Find S1 and S2.
(b) Find T1 and T2. (c) Find a and d.
(d) Find Tn. (e) Find n if Sn = −11.
9. (a) For the arithmetic sequence –7, –4, –1, 2, … 116, fi nd:
(i) a (ii) d (iii) which term has a value of 116 (iv) the number of terms listed (v) the sum of the terms in the sequence
(b) Find the sum of all even natural numbers from 10 to 54, inclusive.
10. (a) An experiment shows that as dry air moves upwards in the atmosphere above the Arctic, it cools about 2 °C for every 100 m rise.
(i) Copy and complete the table below:
Height n above the ground in hundreds of metres 12345 Temperature Tn in °C
20
(ii) Write down a formula connecting Tn and n. (iii) Find the temperature at 1·8 km.
