Give the next 5 terms for each arithmetic sequence. 1. a = 6, d = 3 2. a = 58, d = -7 3. a = 5, d = -2
Answer (1)
To find the next 5 terms of an arithmetic sequence, you need to know the first term a and the common difference d . The formula to find the n -th term of an arithmetic sequence is given by:
T n = a + ( n − 1 ) d
Let's solve each of the given sequences step-by-step:
First Sequence : a = 6 , d = 3
The first term T 1 = 6
Second term T 2 = 6 + 3 = 9
Third term T 3 = 9 + 3 = 12
Fourth term T 4 = 12 + 3 = 15
Fifth term T 5 = 15 + 3 = 18
Sixth term T 6 = 18 + 3 = 21
Thus, the next five terms are: 9, 12, 15, 18, 21.
Second Sequence : a = 58 , d = − 7
The first term T 1 = 58
Second term T 2 = 58 − 7 = 51
Third term T 3 = 51 − 7 = 44
Fourth term T 4 = 44 − 7 = 37
Fifth term T 5 = 37 − 7 = 30
Sixth term T 6 = 30 − 7 = 23
Thus, the next five terms are: 51, 44, 37, 30, 23.
Third Sequence : a = 5 , d = − 2
The first term T 1 = 5
Second term T 2 = 5 − 2 = 3
Third term T 3 = 3 − 2 = 1
Fourth term T 4 = 1 − 2 = − 1
Fifth term T 5 = − 1 − 2 = − 3
Sixth term T 6 = − 3 − 2 = − 5
Thus, the next five terms are: 3, 1, -1, -3, -5.
In each step, we added the common difference d to find the subsequent term.
