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Question: The number of common terms to the two A.P's 17 + 21 + 25 + …..+ 417 and16 + 21 + 26 + …..+ 466 is...

The number of common terms to the two A.P's

17 + 21 + 25 + …..+ 417 and16 + 21 + 26 + …..+ 466 is

A

20

B

19

C

21

D

18

Answer

20

Explanation

Solution

d1 = 4, d2 = 5, first common term = 21

A.P. of common terms is

21 + 41 + 61 + …….

Let no. of common term is 'n'

then Tn = 417 = a+ (n –1) d

417 = 21 + (n –1) 20

39620\frac{396}{20}+ 1 = n

n = 19.8 + 1

n = 20.8 Ï N

so number of common terms = 20