The set of all APs forms a two-dimensional space.] 22 Let A (a, d) represent the AP whose first term is a and difference is d a The sum of two sequences T, and U, is defined to be the sequence whose nth term is T, + U,. п Show that for all constants A and , and for all values of a 1, a2, di and d2, the sequence 2A (a1,d1 HA (a2, d2) is an AP, and find its first term and common difference b Write out the sequences A (1, 0) and A (0, 1). Show that any AP A (a, d) with first term a and difference d can be written in the form A A (1,0) A (0, 1), and find A and u

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QUESTION IS ATTACHED 

(PLEASE DO PART B ONLY I HAVE COMPLETED PART A ?)

The set of all APs forms a two-dimensional space.]
22
Let A (a, d) represent the AP whose first term is a and difference is d
a The sum of two sequences T, and U, is defined to be the sequence whose nth term is T, + U,.
п
Show that for all constants A and , and for all values of a 1, a2, di and d2,
the
sequence
2A (a1,d1 HA (a2, d2) is an AP, and find its first term and common difference
b Write out the sequences A (1, 0) and A (0, 1). Show that any AP A (a, d) with first term a and
difference d can be written in the form A A (1,0) A (0, 1), and find A and u
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Transcribed Image Text

The set of all APs forms a two-dimensional space.] 22 Let A (a, d) represent the AP whose first term is a and difference is d a The sum of two sequences T, and U, is defined to be the sequence whose nth term is T, + U,. п Show that for all constants A and , and for all values of a 1, a2, di and d2, the sequence 2A (a1,d1 HA (a2, d2) is an AP, and find its first term and common difference b Write out the sequences A (1, 0) and A (0, 1). Show that any AP A (a, d) with first term a and difference d can be written in the form A A (1,0) A (0, 1), and find A and u

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