Question

the first four terms of an AP, whose first term is-2 and the common difference is -2,are (a) -2,0,2,4 ,(b) -2,4,-8,16 ,(c) -2,-4,-6,-8 ,(d) -2,-4,-8,-16.​

Answer 1

Answer:

Given,

a = -2

d = -2

Step-by-step explanation:

First term is a = -2.

Second term is a + d = -2 -2 = -4.

Third term is a + 2d = -2 + 2(-2) = -2 -4 = -6.

Fourth term is a + 3d = -2 + 3(-2) = -2 -6 = -8.

So, the correct option is (c) -2, -4, -6, -8.

Answer 2

Given:

The first term of an AP is -2 and the common difference is -2.

To find:

The first four terms of an AP.

Solution:

The nth term of an AP is determined by the formula:

${n}^{th} term = a + (n - 1)d$

Where, a = first term, d = common difference and n = number of terms.

Now, we have

The first term of the AP, a = -2

and common difference, d = -2

Using the above formula,

The second term of AP is:

${2}^{nd} term = - 2 + (2 - 1) - 2$

${2}^{nd} \: term = - 2 - 2$

${2}^{nd} \: term = - 4$

The third term of AP is:

n = 3,

${3}^{rd} term = - 2 + (3 - 1) - 2$

${3}^{rd} \: term = - 2 - 4$

${3}^{rd} \: term = - 6$

The fourth term of the AP is:

n = 4

${4}^{th} term = - 2 + (4 - 1) - 2$

${4}^{th} \: term = - 2 - 6$

${4}^{th} \: term = - 8$

Thus, the sequence of AP is -2,-4,-6,-8.

Hence, the correct option is (c) -2,-4,-6,-8.