Question

Complete the following patterns:
(i) $40,35,30$, __, __, __
(ii) $0,2,4$, ___ , ___ , ___ .
(iii) $84,77,70$, ___ , ___ , ___ .
(iv) $4.4,5.5,6.6$, ___ , ___ , ___ .
(v) $1,3,6,10$, ___ , ___ , ___ .
(vi) $1,1,2,3,5,8,13,21$, ___ , ___ , ___ . (This sequence is called FIBONACCI SEQUENCE)
(vii) $1,8,27,64$, ___ , ___ , ___ .

Answer 1

$\left(i\right)$ $40,35,30,25,20$

Here the series is decreased with difference $=5$ between each number.

$\left(ii\right)$ $0,2,4,6,8,10$

Here the Series is increased with increment $=2$

$\left(iii\right)$ $84,77,70,63,56,49$

Here the Series is decreased with difference $=7$

$\left(iv\right)$ $4.4,5.5,6.6,7.7,8.8,9.9$

Here the Series is increased with increment $=1.1$

$\left(v\right)$ $1,3,6,10,15,21,28$

Here the Series is increased with increasing increment i.e. $3-1=2,6-=3,10-6=4,15-10=5,21-15=6,28-21=7$

$\left(vi\right)$ $1,1,2,3,5,8,13,21,34,55,89$

Here first 2 numbers add with each other to form next number

Similarly, second and Third number add together and result is the fourth Number and so on.

$\left(vii\right)$ $1,8,27,64,125,216,343$

This Series is the Series of Cubes as $1^3,2^3,3^3,4^3,5^3,6^3,7^3$