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Arithmetic Progressions

Question 10:

Show that a1, a2 … , an , … form an AP where an is defined as below

(i) an = 3 + 4n

(ii) an = 9 − 5n

Also find the sum of the first 15 terms in each case.

Answer:

(i) an = 3 + 4n

a1 = 3 + 4(1) = 7

a2 = 3 + 4(2) = 3 + 8 = 11

a3 = 3 + 4(3) = 3 + 12 = 15

a4 = 3 + 4(4) = 3 + 16 = 19

It can be observed that

a2a1 = 11 − 7 = 4

a3a2 = 15 − 11 = 4

a4a3 = 19 − 15 = 4

i.e., ak + 1ak is same every time. Therefore, this is an AP with co...

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