Question

2*3=6,3*4=10,4*5=14,7*8=?​

Answer 1

Given :-

• 2 * 3 = 6
• 3 * 4 = 10
• 4 * 5 = 14
• 7 * 8 = ?

Solution (1) :-

→ 2 * 3 = 2 + 3 + 1 (odd number) = 6

→ 3 * 4 = 3 + 4 + 3 (next odd number) = 10

→ 4 * 5 = 4 + 5 + 5 (next odd number) = 14

then,

→ 7 * 8 =7 + 8 + 7 (next odd number) = 22 (Ans.)

Solution (2) :-

→ 2 * 3 - 0 = 6 - 0 = 0

→ 3 * 4 - 2 = 12 - 2 = 10

→ 4 * 5 - 6 = 20 - 5 = 14

→ 7 * 8 - 12 = 56 - 12 = 44 (Ans.)

[ Here pattern for 0, 2, 6 , 12 is :- +2, +4, +6. ]

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Answer 2

Given : 2*3=6,3*4=10,4*5=14,7*8=?

To Find :  Missing value

Solution:

2*3=6, 3*4=10, 4*5=14 , 7*8=?

Easiest way to add the missing terms also and making sequence continuous

2 * 3  =  6

3 * 4  =  10     ( 6 + 4)

4  * 5  = 14      (10 + 4)

5 * 6  =  18    ( 14 + 4)

6 * 7  =   22   ( 18 + 4)

7  * 8  =  26   ( 22 +  4)  

or define by

Tₙ   = Tₙ₊₁ * Tₙ₊₂ = 4n - 2

n = 1  =>  2 * 3  = 6

n = 2 => 3 * 4 =  10

n = 6  => 7 * 8  =  4 * 7 - 2  = 26

Another method :

2 * 3  =  6   => 2 * 4  -  2

3 * 4  =  10  => 3 * 4  - 2

4 * 5 = 14  => 4 * 4  - 2  

7 * 8 =  26    => 4 * 7  - 2  

Logic is :

a * (a + 1)   =  4a  -  2

Hence Next term will be 26

or  u can do this like

2  *  3  = 6

3  *  4   = 6   +  2[ (3 - 2)  +  (4 - 3) ]  = 10

4  *  5   = 10   +  2[ (4 - 3)  +  (5 - 4) ]  = 14

7  *  8   = 14   +  2[ (7 - 4)  +  (8 - 5) ]  =  26

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