## 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?

**Solution:-**

We know an = a1 + (n -1)*d , Where an = finding term , a1 = first term, d = second term – first term

20th =

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 a_{1} = 1

and a_{n} = 5n – 4.

To find the sum of the given sequence, use the formula S_{n} = .

S_{n} = . (Substitute a_{1} = 1 and a_{n} = 5n – 4.)

S_{n} = .

## Problem 589

Find the 10th term of an arithmetic sequence if t_{1} = 2.1 and t_{4} = 1.83.

**Solution:-**

1.83 = 2.1+(4-1)d

d = -0.09

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

n10th = 1.29