Mathematics

Grade10

Easy

Question

# The 10^{th} term from the end of the Arithmetic Sequences. -5 , -10 , -15 ,…, -1000 is

- -955
- -945
- -950
- -965

Hint:

### The given question is about arithmetic progression. Arithmetic progression is a sequence of numbers where, the difference between two consecutive terms is constant. We are given the sequence till it’s last term. We are asked to find the 10^{th} term from the last. We will first find the number of terms. Using the information, we will find the required term.

## The correct answer is: -955

### The given sequence is -5, -10, -15, …, -1000

The first term of the progression is denoted by a_{1 }= -5

The common difference is denoted by d.

Let there be n terms in the given series.

We have to find 10^{th} term form the end. So, we will have to subtract 9 from the total number of terms to find the position of the 10^{th} term.

Common difference is the fixed difference between the consecutive numbers of the sequence. We have to add the common difference to the preceding term, to get the next term. It can be negative or positive number. It can also have value zero.

The common difference is

d = -10 – (-5)

= -10 + 5

= -5

The last term is -1000. It is the n^{th} term.

The formula for n^{th} term of an arithmetic progression is given as follows:

a_{n} = a_{1} + (n – 1)d

-1000 = -5 + (n – 1)(-5)

-1000 = -5 -5n + 5

-1000 = -5n

Rearranging and dividing both the sides by – 1 we get,

5n = 1000

n = 200

As n = 200, there are 200 terms in the given sequence.

Now, n – 9 = 200 – 9

= 191

So, we have to find 191^{th} term.

a_{191} = -5 + (191– 1)(-5)

= -5 - 950

= -955

So, the 10th term from the end is -955.

For such questions, we should know the formula to find any number lf term. The other way to solve the question, is to consider the last term as first term. We can find the common difference using the given terms. Using this data, we can find the required term.