Question

Find the missing terms of A.P. :
□, 38, □, □, □, –22​

Answer 1

Given :–

• An A.P. (Arithmetic Progression), □, 38, □, □, □, –22.
• a₂ = 38.
• a₆ = –22.

To Find :–

• The missing terms :- a, a₃, a₄, a₅.

Solution :–

First, we need to find the common difference (d),

For this Arithmetic Progression (A.P.),

• a₂ = 38

• a₆ = –22

We know that,

↣ $\sf \: a_{n} = a + (n - 1)d$

Here,

• n = 2

↣ $\sf \: a_{2} = a + (2 - 1)d$

Given that,

• a₂ = 38

↣ $\sf \: 38 = a + 1d$

↣ $\sf38 = a + d$

Now,

• n = 6

↣ $\sf \: a_{6} = a + (6 - 1)d$

Given that,

• a₆ = –22

↣ $\sf - 22 = a + (6 - 1)d$

↣ $\sf - 22 = a + 5d$

Now, subtract eqn. (1) and (2), we obtain

↣ $\sf - 60 = 4d$

↣ $\sf \dfrac{ \cancel{- 60}}{ \cancel{4}} = d$

↣ $\sf - 15 = d$

• d = –15.

Now, we have to find the missing terms.

➲ a = a₂ – d

• a₂ = 38
• d = –15

↣ 38 – (–15)

↣ 38 + 15

↣ 53

➲ a₃ = a + 2d

• a = 53
• d = –15

↣ 53 + 2(–15)

↣ 53 – 30

↣ 23

➲ a₄ = a + 3d

• a = 53
• d = –15

↣ 53 + 3(–15)

↣ 53 – 45

↣ 8

➲ a₅ = a + 4d

• a = 53
• d = –15

↣ 53 + 5(–15)

↣ 53 – 60

↣ –7

Hence,

The missing terms are 53, 23, 8 and –7 respectively.

Check :–

For checking, we need to find the common difference (d) between all the terms.

If the common differences (d) are same then the answer is correct.

So,

a₆ – a₅ = a₅ – a₄ = a₄ – a₃ = a₃ – a₂ = a₂ – a

• a = 53
• a₂ = 38
• a₃ = 23
• a₄ = 8
• a₅ = –7
• a₆ = –22

Now,

↣ –22 – (–7) = –7 – 8 = 8 – 23 = 23 – 38 = 38 – 53

↣ –22 + 7 = –15 = –15 = –15 = –15

↣ –15 = –15 = –15 = –15 = –15

Since, all the common difference is equal.

So, the missing numbers 53, 23, 8 and –7 is correct.

Answer 2

Answer:

53,38,-23,-8,-7

Step-by-step explanation:

I hope this answer may help you