Question

Each question is follewed by four choices for an answer. Read each question and then decide for the best answer. Provide complete Solution for each item.

1. If three arithmetic means are inserted between — 15 and 9, What is the first of the arithmetic.

A. 3
B. - 3
C. - 9
D. 6

2. Which of the following is the nth term of the arithmetic sequence 1, 8, 17, 26, ... ?

$\sf{A. \: \green{ a_{n} \: = 10n \: - 9 }}\\ \ \textless \ br /\ \textgreater \ \sf{B. \: \green{a_{n} = 10n + 9 }} \\ \ \textless \ br /\ \textgreater \ \sf{C. \green{ \: a_{n} = 9n + 1C}} \\ \sf{D. \: \green{ a_{n} = 9n - 10}}$
$\small\bold3 . \: \rm{\: a _{n} = 13n - 3 \: is \: the \: nth \: term } \\ \small \rm{\: of \: the \: arithmetic \: sequence,} \\ \small\rm{what \: is \: it \: 5th \: term?}$
A. 65
B. 62
C. 49
D. 36

4. What is the nth term of the arithmetic sequence 7, 6, 5, 4, ...?

$\sf{A. \green{\: a_{n}=8-n}}\\ \sf{B.\green{ \: a_{n}=7n-3}}\\ \sf{C. \green{\: a_{n}=5n +2}} \\ \sf{D. \green{\: a_{n}=10-3n}}$
5. If five arithmetic means are inserted between 11 and 53, What is the third of the arithmetic means.

A. 25
B. 32
C. 39
D. 46


— Nonsense Reported —
​

Answer 1

Step-by-step explanation:

Mean of 5 numbers =18

⇒ Sum of these 5 numbers =18×5=90

Let number that has been excluded be x

New mean =

4

90−x

=16

Solving this, we get

90−x=64

∴x=26

Answer 2

EXPLANATION.

Question = 1.

Three arithmetic means.

Inserted between = - 15 and 9.

As we know that,

Formula of :

Inserting N means between two numbers.

⇒ d = (b - a)/(n + 1).

⇒ a = - 15   and   b = 9.

⇒ n = 3.

⇒ d = (9 - (-15))/(3 + 1).

⇒ d = (9 + 15)/4.

⇒ d = 24/4.

⇒ d = 6.

Now, we write equation as,

⇒ A₁ = a + d.

⇒ A₁ = - 15 + 6.

⇒ A₁ = - 9.

Option [C] is correct answer.

Question = 3.

⇒ Aₙ = 13n - 3.

As we know that,

To find : 5th term.

⇒ a₅ = 13(5) - 3.

⇒ a₅ = 65 - 3.

⇒ a₅ = 62.

Option [B] is correct answer.

Question = 4.

Arithmetic sequences = 7, 6, 5, 4, . . . . .

As we know that,

First term = a = 7.

Common difference = d = b - a = c - b = 6 - 7 = - 1.

As we know that,

Formula of General term of an A.P.

⇒ Tₙ = a + (n - 1)d.

⇒ Tₙ = 7 + (n - 1)(- 1).

⇒ Tₙ = 7 + (- n) + 1.

⇒ Tₙ = 8 - n.

Option [A] is correct answer.

Question = 5.

Five arithmetic means.

Inserted between = 11 and 53.

As we know that,

Inserting N means between two numbers.

⇒ d = (b - a)/(n + 1).

⇒ a = 11   and   b = 53.

⇒ n = 5.

⇒ d = (53 - 11)/5 + 1.

⇒ d = (42)/6.

⇒ d = 7.

⇒ Aₙ = a + nd.

To find : 3rd arithmetic means.

⇒ A₃ = 11 + 5(7).

⇒ A₃ = 11 + 35.

⇒ A₃ = 46.

Option [D] is correct answer.