Mathematics
Grade10
Easy
Question
The 10th 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 10th 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 a1 = -5
The common difference is denoted by d.
Let there be n terms in the given series.
We have to find 10th term form the end. So, we will have to subtract 9 from the total number of terms to find the position of the 10th 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 nth term.
The formula for nth term of an arithmetic progression is given as follows:
an = a1 + (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 191th term.
a191 = -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.
