Math, asked by ibadgerphotography18, 11 months ago

Write the first four terms of the AP when the first term and common difference as follows.


(a) a = -1 and d =

−1/2



(b) a = 4 and d = -3​

Answers

Answered by RvChaudharY50
39

Arithmetic progression :-

• A sequence is said to be in AP (Arithmetic Progression), if the difference between its consecutive terms are equal.

• The nth term of an AP is given as ;

T(n) = a + (n-1)•d , where a is the first term and d is the common difference.

• The common difference of an AP is given as ;

d = T(n) - T(n-1)

• If the number of terms in an AP is n ( where n is odd ) ,then there will be a single middle term.

Also, [(n+1)/2]th term will be its middle term.

• If the number of terms in an AP is n ( where n is even ) ,then there will be two middle terms.

Also, (n/2)th and (n/2 + 1)th terms will be its middle terms.

• The sum up to nth terms of an AP is given as ;

S(n) = (n/2)•[2a + (n-1)•d] where a is the first term and d is the common difference.

• The nth term of an AP is also given as ;

T(n) = S(n) - S(n-1)

___________________

Solution :-

(a)

First term = a = (-1)

→ common difference = d = (-1/2)

So,

T₂ = a + (n - 1)d

→ T₂ = (-1) + (2 - 1)(-1/2)

→ T₂ = (-1) + (-1/2)

→ T₂ = (-3/2) = second Term of AP .

Similarly,

T₃ = T₂ + d or, = a + (n - 1)d

→ T₃ = (-1) + (3 - 1) * (-1/2)

→ T₃ = (-1) + 2 * (-1/2)

→ T₃ = (-1) + (-1)

→ T₃ = (-2) = Third Term of AP.

Similarly,

T₄ = T₃ + d

→ T₄ = (-2) + (-1/2)

→ T₄ = (-5/2) = Fourth Term of AP.

Hence, The Required AP will be :- (-1) , (-3/2) , (-2) , (-5/2).

____________________

(b)

→ First term = a = 4

→ common difference = d = (-3)

So,

→ T₂ = a + (n - 1)d

→ T₂ = 4 + (2 - 1)(-3)

→ T₂ = 4 - 3

→ T₂ = 1 = second Term of AP .

Similarly,

→ T₃ = T₂ + d or, = a + (n - 1)d

→ T₃ = 4 + (3 - 1) * (-3)

→ T₃ = 4 + 2 * (-3)

→ T₃ = 4 + (-6)

→ T₃ = (-2) = Third Term of AP.

Similarly,

→ T₄ = T₃ + d

→ T₄ = (-2) + (-3)

→ T₄ = (-5) = Fourth Term of AP.

Hence, The Required AP will be :- 4 , 1 , (-2) , (-5).

_____________________

Answered by VishnuPriya2801
25

Answer:-

(a) Given:

a = - 1

d = - 1/2.

We know that,

nth term of an AP = a + (n - 1)d

We already have a 1 → - 1

To find 2nd term put the value of n as 2.

→ a(2) = - 1 + (2 - 1)( - 1/2)

→ a(2) = - 1 - 1/2

a(2) = (- 2 - 1)/2 = - 3/2

Similarly,

a(3) = - 1 + (3 - 1)(- 1/2)

→ a(3) = - 1 + (2)(- 1/2)

→ a(3) = - 1 - 1

a(3) = - 2

a(4) = - 1 + (4 - 1)( - 1/2)

→ a(4) = - 1 - 3/2

a(4) = (- 2 - 3)/2 = - 5/2.

(b) a = 4

d = - 3

a(2) = 4 + (2 - 1)( - 3)

→ a(2) = 4 - 3

a(2) = 1

a(3) = 4 + (3 - 1)( - 3)

→ a(3) = 4 - 6

a(3) = - 2

a(4) = 4 + (4 - 1)( - 3)

→ a(4) = 4 - 9

a(4) = - 5

Therefore,

From (a) - The first 4 terms are - 1 , - 3/2 , - 2 , - 5/2.

From (b) - The first 4 terms are 4 , 1 , - 2 , - 5.

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