Mathematics
Easy

Question

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

Hint:

## The correct answer is: -955

### The given sequence is -5, -10, -15, …, -1000The first term of the progression is denoted by a1 = -5The 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 isd = -10 – (-5)= -10 + 5= -5The 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 = -5nRearranging and dividing both the sides by – 1 we get,5n = 1000n = 200As n = 200, there are 200 terms in the given sequence.Now, n – 9 = 200 – 9= 191So, we have to find 191th term.a191 = -5 + (191– 1)(-5)= -5 - 950= -955So, 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.