Question

Find the second term, if first, third and fourth terms are 15, 27, 63

Answer 1

(i) 6 : 8 and 12 : 16

6 : 8 = 6/8 = 3/4

12 : 16 = 12/16 = 3/4

Thus, the ratios 6 : 8 and 12 : 16 are equal.

Therefore, they form a proportion.

(ii) 24 : 28 and 36 : 48

24 : 28 = 24/28 = 6/7

36 : 48 = 36/48 = 3/4

Thus, the ratios 24 : 28 and 36 : 48 are unequal.

Therefore, they do not form a proportion.

Answer 2

Let the Second term be x
Now If we will replace with x it will form
15 : x : 27 : 63
Now,
Product of means = Product of Extremes
x × 27 = 15 × 63
27x = 945
x = 945/27
x =35
So , the Second term will be 35