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Solution


Q.

4 groups in a class were asked to come up with an arithmetic progression (AP).
Shown below are their responses:

 

(i) Group M → [4, 2, 0, –2, …]
(ii) Group N → [41, 38.5, 36, 33.5, …]
(iii) Group O → [–19, –21, –23, –25, …]
(iv) Group P → [–3, –3, –3, –3, …]

 

Which of these groups correctly came up with an AP
1 (i) and (iii)  
2 (ii) and (iii)  
3 (i), (ii) and (iii)  
4 All are correct  

Ans.

(4)

For Group M, we have 4, 2, 0, -2, ....
Now, IInd term – Ist term = 2 – 4 = -2 = 0 – 2 = IIIrd term – IInd term.

∴ It is an AP ⇒ Group M is correct

For Group N, we have 41, 38.5, 36, 33.5 ....
Now, IInd term – Ist term = 38.5 – 41 = -2.5 = 36 – 38.5 = IIIrd term – IInd term.
∴ It is an AP ⇒ Group N is correct.

For Group O, we have -19, -21, -23, -25 ....
= -21 – (-19) = -23 – (-21) = -2
Now, IInd term – Ist  term = IIIrd term – IInd term = -2
∴ It is an AP ⇒ Group O is correct.

For Group P, we have -3, -3, -3, -3 ....
 -3 – (-3) = -3 – (-3) = 0
Now, IInd term – Ist term = IIIrd term – IInd term = 0
∴ It is an AP ⇒ Group P is correct