You inspect the series that you have, very carefully.
-- You notice that 9 was <em><u>increased by 2</u></em> to get 11.
-- You notice that 11 was <em><u>increased by 2</u></em> to get 13.
-- You notice that 13 was <em><u>increased by 2</u></em> to get 15.
-- You notice that 15 was <em><u>increased by 2</u></em> to get 17.
By now, it begins to dawn on you. You say to yourself "Self ! I'll just bet
that each term has to be increased by 2 in order to get the next term."
Acting on that assumption, you set out on your flight of prediction:
-- You take the last term, 17, increase it by 2,and get 19.
-- You take the new term that you have created, 19,
increase it by 2, and get 21.
-- You take the 2nd new term that you have created, 21,
increase it by 2, and get 23.
Now you have the three new terms, and that's all you were asked for.
But you're just getting warmed up. Nothing can stop you now.
25, 27, 29, 31, 33, 35, 37, 39, 41, 43, 45, 47, 49,
51, 53, 55, 57, 59, 61, 63, 65, 67, 69, 71, 73, 75,
77, 79, 81, 83, 85, 87, 89, 91, 93, 95, 97, 99, 101
Suddenly, you stop ! You just realized that this is not the ONLY
possible pattern that would produce the same first 5 numbers.
Answer: The required length of the golden thread needed is 30 cm.
Step-by-step explanation: Given that a triangular colorful scenery is made in a wall with sides 50 cm, 50 cm and 80 cm. A golden thread is to hang from the vertex so as to just reach the side 80 cm.
We are to find the length of the golden thread required.
As shown in the attached figure below, ABC is the triangular scenery with sides
AB = AC = 50 cm and BC = 80 cm.
AD is drawn perpendicular to BC, so that AD is the length of the golden thread required to reach side BC with length 80 cm from the vertex A.
Now, since AD ⊥ BC and ΔABC is isosceles (AB = AC), so we must have
D is the midpoint of BC.
That is,

Now, from the right-angled triangle ABD, we have

Thus, the required length of the golden thread needed is 30 cm.
3. 5/12 * 4/9 = 5/27
4. x - 2 2/5 = 5 13/20
x - 12/5 = 113/20
x = 113/20 + 12/5
x = 113/20 + 48/20
x = 161/20 or 8 1/20