Question

The first three terms of an arithmetic sequence are as follows.-1, 3, 7Find the next two terms of this sequence

Answer 1

11 and 15

Explanations:

Given the arithmetic sequence -1, 3, 7 __, __, you are to find the next two terms of the sequence.

The nth term of an arithmetic sequence is given as;

`T_n=a+(n-1)d`

where:

• a is the ,first term

,

• n is the ,number of terms

,

• d is the ,common difference

From the given sequence;

a = -1

d = 3 - (-1) = 7 - 3 = 4

For the fourth term, n = 4;

`\begin{gathered} T_4=-1+(4-1)\cdot4 \\ T_4=-1+3(4) \\ T_4=-1+12 \\ T_4=11 \end{gathered}`

For the fifth term, n = 5;

`\begin{gathered} T_5=-1+(5-1)\cdot4 \\ T_5=-1+4(4) \\ T_5=-1+16 \\ T_5=15 \end{gathered}`

Therefore the next two terms of the arithmetic sequence are 11 and 15.