The question is given from ncert Book of class 10th Chapter no. 5 Ex. 5.2 Q. 17. In the following question you have to find the 20th term from the last in the given A.P. Also give the solution with brief details.

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Solution:The given A.P. is 3, 8, 13, …, 253

d= 5

We can also write the given Arithmetic Progression in reverse order as;

253, 248, 243, …, 13, 8, 5

For the new A.P,

a = 253

d = 248 − 253 = −5

n = 20

i.e using nth term formula, we get,

a_{20}=a+(20−1)da_{20}= 253+(19)(−5)a_{20}= 253−95a= 158i.e 20th term from the last term of the Arithmetic Progression is 158.