HOW TO FIND THE NEXT THREE TERMS IN A SEQUENCE

Find the next three terms of each sequences of each sequence. Next to the problem, describe the pattern in words.

Problem 1 :

4, -16, 64, -256, 1024,…

A) -1024, 4096, -16384          B) -4096, -16384, -65536

C) - 4096, 16384, -65536       D) -1024, -4096, -16384

Solution :

To find the next three, first we have to find out the pattern followed in sequence.

Pattern :

2^nd term ==>  4(-4)  ==>  -16

3^rd term ==>  -16(-4)  ==>  64

4^th term ==>  64(-4)  ==>  -256

5^th term ==>  -256(-4)  ==>  1024

6^th term = -4(1024) = -4096

7^th term = 4(4096) = 16384

8^th term = -4(16384) = -65536

Hence the next three terms are -4096, 16384, -65536.

So, option (C) is correct.

Problem 2 :

1, 5, 25, 125, 625,…

A) 6250, 31250, 156250         B) 3125, 15625, 78125

C) 2/3125, 2/15625, 2/78125       D) 2/625, 2/3125, 2/15625

Solution :

Pattern followed :

Every term is being multiplied by 5.

6^th term = 5(625) = 3125

7^th term = 5(3125) = 15625

8^th term = 5(15625) = 78125

Hence the next three terms are 3125, 15625, 78125.

So, option B) is correct.

Problem 3 :

4, 16, 36, 64, 100,…

A) 144, 196, 281        B) 144, 196, 256

C) 164, 196, 307        D) 144, 196, 300

Solution :

To find the next three, first we have to find out the pattern followed in sequence.

Pattern :

4 = 2²_,  16 = 4²_,  36 = 6²_, 64 = 8²_, 100 = 10²

So, the next three terms will be 12², 14², 16².

Hence the next three terms will be 144, 196, 256.

So, option B) is correct.

Problem 4 :

4, -12, 36, -108, 324,…

A) -972, -2916, -8748              B) -972, 2916, -8748

C) -4/243, 4/729, -4/2187       D) -4/243, -4/729, -4/2187

Solution :

To find the next three, first we have to find out the pattern followed in sequence.

Pattern :

Multiplying the first term by -3, we get the second term. Multiplying the second term by 3, we get the third term.

6^th term = -3(324) = -972

7^th term = 3(972) = 2916

8^th term = -3(2916) = -8748

Hence the next three terms are -972, 2916, -8748.

So, option B) is correct.

Problem 5 :

1, 9, 25, 49, 81,…

A) 121, 169, 225            B) 121, 193, 225

C) 140, 160, 225            D) 167, 160, 225

Solution :

To find the next three, first we have to find out the pattern followed in sequence.

Pattern :

The square of odd numbers is the pattern.

1 = 1²_,  9 = 3²_, 25 = 5²_, 49 = 7²_, 81 = 9²

6^th term = 11² ==> 121

7^th term = 13² ==> 169

9^th term = 15² = 225

Hence the next three terms are 121, 169, 225.