Question

class 10 maths arithmetic progression​

Answer 1

Step-by-step explanation:

Let the first term be a and the common difference be d.

Since, the A.P. contains 37 terms, the middle term is term. ((37 + 1)/2) ^ (th) = 19 ^ (th)

According to the question,

a_{18} + a_{19} + a_{20} = 225

(a+(18-1)d)+(a+(19-1)

3a+17d+18d+19d=225

3a+54d=225

3(a+18d)=225

a+18d= 225 3

a+18d=75

a=75-18d.. (1)

Also,a_{35} + a_{36} + a_{37} = 429

(a+(35-1)d)+(a+(36-1).

3a+34d+35d+36d=429

3a+105d=429

3(a+35d)=429

a+35d= 429 3

75-18d+35d=143 ( from (1)

17d=143-75

17d=68

d=4

a=75-18(4)(from (1))

a=75-72

a=3

Hence, the resulting A.P is 3,7,12......

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