**How to find the next three terms in arithmetic sequence :**

In an arithmetic sequence, in order to get the next term we have to add (or) subtract the common difference with the previous term.

Let us look in to some example problems to understand the above concept.

**Example 1 :**

Find the next three terms of each arithmetic sequence.

4, 7, 10, 13, …

**Solution :**

Common difference :

d = a_{2} - a_{1}

= 7 - 4

= 3

In order to get 5^{th} term, we have to add the common difference 3 with the 4^{th} term.

a = 13 + 3 a |
a = 16 + 3 a |
a = 19 + 3 a |

Hence the next three terms of the above sequence are 16, 19 and 21.

**Example 2 :**

Find the next three terms of each arithmetic sequence.

18, 24, 30, 36, …

**Solution :**

Common difference :

d = a_{2} - a_{1}

= 24 - 18

= 6

In order to get 5^{th} term, we have to add the common difference 3 with the 4^{th} term.

a = 36 + 6 a |
a = 42 + 6 a |
a = 48 + 6 a |

Hence the next three terms of the above sequence are 42, 48 and 54.

Let us see the next example on "How to find the next three terms in arithmetic sequence".

**Example 3 :**

Find the next three terms of each arithmetic sequence.

-66, -70, -74, -78, …

**Solution :**

Common difference :

d = a_{2} - a_{1}

= -70 - (-66)

= -70 + 66

= -4

In order to get 5^{th} term, we have to add the common difference 3 with the 4^{th} term.

a = -78 + (-4)
a |
a = -82 + (-4)
a |
a = -86 + (-4) = -86 -4 a |

Hence the next three terms of the above sequence are -82, -86, and -90.

**Example 4 :**

Find the next three terms of each arithmetic sequence.

-31, -22, -13, -4, …

**Solution :**

Common difference :

d = a_{2} - a_{1}

= -22 - (-31)

= -22 + 31

= 9

In order to get 5^{th} term, we have to add the common difference 3 with the 4^{th} term.

a = -4 + 9 a |
a = 5 + 9 a |
a = 14 + 9 a |

Hence the next three terms of the above sequence are 5, 14 and 23.

After having gone through the stuff given above, we hope that the students would have understood "How to find the next three terms in arithmetic sequence".

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