Posts Tagged ‘arithmetic sequence’

Problem 686

 

Write the arithmetic sequence that has four arithmetic means between -20 and 20.

 

Solution:-

 

The rule of arithmetic sequence

{a, a+d, a+2d, a+3d, … }

a = -20

6th term = 20

a+5d = 20

-20+5*d = 20

d = 8

four arithmetic means between -20 and 20

-12,-4,4,12

 

Problem 637

What is the 20th term of the following arithmetic sequence?

\frac{1}{2},1,\frac{3}{2},2,....

 

Solution:-

 

We know an = a1 + (n -1)*d , Where an = finding term , a1 = first term, d = second term – first term
20th = \frac{1}{2}+(20-1)*\frac{1}{2}
20th = 10
So the value of the 20th term 10.

 

Problem 634

What is the 25th term in the following arithmetic sequence?
-7, -2, 3, 8, …

 

Solution:-

 

We know an = a1 + (n -1)*d ,

Where an = finding term , a1 = first term, d = second term – first term
25th = -7 + (25 – 1) * 5
25th = 113
So the value of 25th term 113

 

Problem 633

What are the next four terms in the following arithmetic sequence?
-7, -2, 3, 8, …

 

Solution:-

 

First we find the value of d = -2 – (-7) = 5
Now we add value of d find the next number
13, 18, 23, 28

Problem 632

What is the d value in the following arithmetic sequence?
-7, -2, 3, 8, …

Solution:-

The value of d = second term – first term

d = -2 – (-7)
d = 5

Problem 599

 

Find the sum.

1 + 6 + 11+ ……+(5n – 4)

 

Solution :-

 

We are given an arithmetic sequence. The first last terms of this sequence are a1 = 1

and  an = 5n – 4.

To find the sum of the given sequence, use the formula Sn = \frac{n}{2}(a_{1}+a_{n}).

Sn = \frac{n}{2}(1+5n-4). (Substitute a1 = 1 and an = 5n – 4.)

Sn = \frac{n}{2}(5n-3).

 

Problem 589

 

Find the 10th term of an arithmetic sequence if t1 = 2.1 and t4 = 1.83.

 

Solution:-

 

1.83 = 2.1+(4-1)d

d = -0.09

n10th = 2.1+(10-1)*(-0.09)

n10th = 1.29