**How to Find the Next Three Terms in a Sequence :**

Here we are going to see some practice questions to find the next three terms in a sequence.

There is some arrangement or pattern followed in every sequence.

There are two types of sequence,

**Finite sequence :**

If the number of elements in a sequence is finite then it is called a Finite sequence.

**Infinite sequence :**

If the number of elements in a sequence is infinite then it is called an Infinite sequence.

**Question 1 :**

Find the next three terms of the following sequence.

(i) 8, 24, 72, …

**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.

4^{th} term = 3 (72) = 216

5^{th} term = 216 (3) = 648

6^{th} term = 648(3) = 1944

Hence the next three terms are 216, 648, 1944.

(ii) 5, 1,-3,…

**Solution :**

**Pattern :**

By subtracting 4 from the 1^{st} term, we get second term. By subtracting 4 from 2^{nd} term, we get 3^{rd} term.

4^{th} term = -3 - 4 = -7

5^{th} term = -7 - 4 = -11

6^{th} term = -11 - 4 = -15

Hence the next three terms are -7, -11, -15.

(iii) 1/4, 2/9, 3/16,…

**Solution :**

**Pattern :**

General term = n [1/(n + 1)]^{2}

n is elements of natural numbers.

4th term = 4 [1/(4 + 1)]^{2}

= 4[1/5]^{2}

= 4/25

5th term = 5 [1/(5 + 1)]^{2}

= 5[1/6]^{2}

= 5/36

6th term = 6 [1/(6 + 1)]^{2}

= 6[1/7]^{2}

= 6/49

Hence the next three terms are 4/25, 5/36, 6/49.

**Question 1 :**

Find the first four terms of the sequences whose nth terms are given by

(i) a_{n} = n^{3} −2

**Solution :**

To find the 1st term, we have to apply n = 1

a n = 1 a = 1 - 2 a |
a n = 2 a = 8 - 2 a |

a n = 3 a = 27 - 2 a |
a n = 4 a = 64 - 2 a |

Hence the first four terms are -1, 6, 25, 62.

(ii) a_{n} = (−1)^{n+1} n(n + 1)

**Solution :**

a n = 1 = (−1) = (−1) = 1 (2) a |
n = 2 = (−1) = (−1) = -1 (6) a |

n = 3 = (−1) = (−1) = 1 (12) a |
n = 4 = (−1) = (−1) = -1 (20) a |

Hence the first four terms are 2, -6, 12, -20.

(iii) a_{n} = 2n^{2} - 6

**Solution :**

a n = 1 = 2(1) a |
a n = 2 = 2(2) a |

a n = 3 = 2(3) a |
a n = 4 = 2(4) a |

Hence the four terms are -4, 2, 12, 26.

After having gone through the stuff given above, we hope that the students would have understood, "How to Find the Next Three Terms in a Sequence".

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