Question

What is the next term of the arithmetic sequence 5, 2, - 1, ____?
A. – 7 B. – 6 C. – 4 D. – 3

Answer 1

Answer:

C. -4

Step-by-step explanation:

a=5

d= 3-5 = -2

a4 = a+3d= 5+ 3(-3)= 5-9 = -4

Answer 2

• Option C. –4 is correct.

Given :–

Three terms :

• First term = $\sf a_{1}$ = 5.
• Second term = $\sf a_{2}$ = 2.
• Third term = $\sf a_{3}$ = –1.

To Find :–

• The next term.

Solution :–

First, we need to find the common difference.

Common difference (d) = $\sf a_{2} - a_{1} = a_{3} - a_{2}$

So,

We have,

• $\sf a_{1} = 5$
• $\sf a_{2} = 2$
• $\sf a_{3} = -1$

$\longmapsto d = 2 - 5= - 1 - 2$

$\longmapsto d = - 3 = - 3$

Hence, the common difference (d) is –3.

Now, we have to find the next term $\sf (a_{4}).$

So,

Next term = $\sf a_{3} + common \: difference \: (d)$

We have,

• $\sf a_{3} = -1$
• Coming difference (d) = –3.

$\longmapsto a_{4} = - 1 + ( - 3)$

$\longmapsto a_{4} = - 1 - 3$

$\longmapsto a_{4} = - 4$

Hence,

The next term is –4.

So, the option C. –4 is correct.

Verification :–

Common difference (d) = –3.

$\longmapsto a_{4} - a_{3} = - 3$

We have,

• $\sf a_{3} = -1$
• $\sf a_{4} = -4$

$\longmapsto - 4 - ( - 1) = - 3$

$\longmapsto - 4 + 1 = - 3$

$\longmapsto - 3 = - 3$

Hence Verified !!