Question

the ratio of 11th term to 18th term of an AP is 2:3 .Find the ratio of the 4th term to 21st term and also the ratio of sum of first 5 terms to the sum of first 21st terms

Answer 1

◆ Arithmetic Progressions ◆

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Answer 2

a11 = a+10d
a18 = a+17d

a+10d 2
_____= ___
a+17d 3

So, we can cross multiply this.

=> 3(a+10d) =2(a+17d)
=> 3a+30d = 2a+34d
=> a = 4d

a4 = a+3d
a21 = a+20d

a4:a21 = (a+3d) / (a+20d)
Putting value of 'a' here, we get

=> (4d+3d) / (4d+20d)
=> 7d / 24d
=> 7:24


Sn = n/2 [ 2a + (n-1)d]
Sum of first 5 terms = 5/2 [2×a + (5-1)d]
= 5/2 [2×4d +4d] = 5/2[12d]
= 5×6d = 30d

Sum of first 21 terms = 21/2 [2×a + (21-1)d]
= 21/2[2×4d +20d] = 21/2[28d]
= 21×14d = 294d

=> 30d/294d
=> 5/49
So, ratio will be = 5:49