Answer:
A) 65
B) 5
C) 242
D) 531
E) 36
Step-by-step explanation:
A) Let the unknown term be x.
Difference between 5 & 9 = 4
Difference between 9 & 17 = 8 = 4×2
Difference between 17 & 33 = 16 = 8×2
It is observed that the difference between two terms is getting doubled. So,
Difference between 33 & x = 16×2 = 32
∴ x = 33 + 32 = 65
B) Let the unknown term be x.
Difference between 20 & 12 = 8
Difference between 12 & 8 = 8/2 = 4
Difference between 8 & 6 = 4/2 = 2
It is observed that the difference between two terms is getting halved.
Difference between 6 & x = 2/2 = 1
∴ x = 6 - 1 = 5
C) Let the unknown term be x.
Difference between 2 & 8 = 6
Difference between 8 & 26 = 18 = 6×3
Difference between 26 & 80 = 54 = 18×3
It is observed that the difference between two terms is getting tripled.
Difference between 80 & x = 54×3 = 162
∴ x = 80 + 162 = 242
D) Let the unknown term be x.
Difference between 36 & 69 = 33
Difference between 69 & 135 = 66 = 33×2
Difference between 135 & 267 = 132 = 66×2
It is observed that the difference between two terms is getting doubled.
Difference between 267 & x = 132×2 = 264
∴ x = 267 + 264 = 531
E) Let the unknown term be x.
4 = 2²
9 = 3²
16 = 4²
25 = 5²
It is observed that all the terms in the sequence are squares of consecutive natural numbers.
So, x = 6² = 36
and 
. We see that c = 5. We need now to find the secant of that right triangle. Secant if the co-identity of cosine which is side adjacent over hypotenuse. That means that secant is the hypotenuse over the side adjacent. So our secant theta = 5/4