Question

write the arithmetic progression when first term a and common difference d are as follows: a = -1, d = 1/2​

Answer 1

Solution

Given :-

• First terms of A.P. (a) = -1
• Common difference (d) = 1/2

Find :-

• Series of A.P.

Explanation

Using Formula,

★ Nth terms of A.P. = a + (n-1)d

Where,

• a = first terms
• n = Number of terms
• d = common difference

We, calculate second terms

➡ a2 = a + (2-1)d

➡a2 = a + d

keep value of a & d

➡a2 = -1 + 1/2

➡a2 = (-2+1)/2

➡a2 = -1/2

_______________________

Now, calculate third terms

➡a3 = a + 2d

keep value of a & d

➡a3 = -1 + 2 × 1/2

➡a3 = -1 + 1

➡a3 = 0

________________________

Now, calculate Fourth terms

➡a4 = a + 3d

keep value of a & d

➡a4 = -1 + 3×1/2

➡a4 = -1 + 3/2

➡a4 = (-2+3)/2

➡a4 = 1/2

_________________________

Now, calculate fifth terms,

➡a5 = a + 4d

keep value of a & d

➡a5 = -1 + 4×1/2

➡a5 = -1 + 2

➡a5 = 1

________________________

Now, calculate sixth terms,

➡a6 = a + 5d

keep value of a & d

➡a6 = -1 + 5×1/2

➡a6 = -1 + 5/2

➡a6 = (-2+5)/2

➡a6 = 3/2

_______________________

Hence

• A.P. series will be , -1 , -1/2, 0 , 1/2 , 1 , 3/2.............

________________

Answer 2

Answer:

answer is -1, -1/2, 0, 1/2, 1.......so on.

Step-by-step explanation:

In arithmetic progressions, to know the nth term, we have a formula which is

an = a + (n-1)d

where,

an is the nth term

a is the first term

d is the common difference

n is the position of the term.

By using this formula, we can get the arithmetic progression.