Question

The 20th term from the last of arithmetic sequence 5, 10, 15, 20 …… 150 will be
a. 25
b. 45
c. 55
d. 85

Answer 1

Hint: As we know that the given series is in AP, we will directly use the formula of AP, that is, l – (n-1)d to find the 20th term from the last of the arithmetic sequence given. Here, l is the last term, n is the given number of terms and d is the common difference.

Complete step-by-step answer:
It is given in the question that we have to find the 20th term from the last of an arithmetic sequence, which is given as, 5, 10, 15, 20 …… 150. In order to solve this question, we will directly use the formula of AP, that is, l – (n-1)d as we are asked to find the 20th term from the last of the arithmetic sequence. Here l is the last term, n is the given number of terms and d is the common difference.
Now, from the given arithmetic sequence we can see that the last term is 150, number of terms required is 20 and the common difference is 5. So, we get, l = 150, n = 20 and d = 5. On substituting these values in the formula, l – (n-1)d, we will get,
150 – (20 - 1)5
150 – 19 $\times $ 5
150 – 95
55
Therefore, the 20th term from the last of the arithmetic sequence 5, 10, 15, 20 …… 150 is 55.
Hence, option (c) is the correct answer.

Note: The most common mistake that the students make while solving this question is that they miss the word ‘last’, so they might end up using the wrong formula, that is, ${{a}_{n}}=a+\left( n-1 \right)d$ as they think that we have to find the 20th term of the arithmetic sequence. But, we are actually supposed to find the 20th term from the last of the arithmetic sequence, so we have to use the formula, l – (n - 1)d. So, the students must read these questions very carefully in order to avoid any mistakes.