Which of the following list of numbers does form an A .P. ? If they form an A .P., write the next two terms.
(i) 6, 1, –4, –9, –14............
(ii) 1, –3, –5...........
(iii) –2. 2. –2, 2, –2.............
(iv) 1, 1, 1, 2, 2, 3, 3,.............

(i) a₂ – a₁ = 1 – 6 = –5
a₃ – a₂ = –4 – 1 = –5
a₄ – a₃ = –9 – (–4) = –9 + 4 = –5
And, a₅ – a₃ = –14 – (–9) = –14 + 9 = 5
Since, the difference between each pair of consecutive terms are constant.
So, the given numbers form an A.P. with the common difference -5.
The next two terms are :
–14 + (–5) = –14 – 5 = –19
–19 + (–5) = –24.
(ii) a₂ – a₁ = –1 – 1 = –2
a₃ – a₂ = –3 – (–1) = –3 + 1 = –2
a₄ – a₃ = –5 – (–3) = –5 + 3 = –2
Since, the difference between each pair of consecutive terms are constant.
So, the given numbers form an A .P. with the common difference -2.
The next two terms are :
–5 + (–2) = –5 – 2 = –7
–7 + (–2) = –7 – 2 = –9.
(iii) a₂ – a₁ = 2 – (–2) = 2 + 2 = 4
a₃ –a₂ = –2 – (2) = –2 – 2 = –4
a₄ – a₃ = –5 – (–3) = –5 + 3 = –2
Since, the difference between each pair of consecutive terms are not constant.
So, the given numbers does not form an A .P.
(iv) a₂ – a, = 1 – 1 = 0
a₃ – a₂ = 1 – 1 = 0
a₄ – a₃ = 2 – 1 = 1
a₅ = 2 – 2 = 0
a₆ – a₅ = 3 – 2 = 1
a₇ – a₆ = 3 – 3 = 0
Since, the difference between each pair of consecutive term are not constant.
So, the given numbers does not form an A .P