Which term of this Arithmetic Progression 3, 8, 13, 18, .… is 78 ?

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This question is from Ncert Book class 10th Ch. number 5 Ex. 5.2 Q. 4 . In the following question you have to find out which term of the A.P given above will be 78. Also give the full solution of the question.

Solution:A.P is given as 3, 8, 13, 18, …

a = 3

d = a

_{2}− a_{1}= 8 − 3 = 5Let the nth term of the A.P. be 78.

We know,

a=_{n}a+(n−1)dThen,

78 = 3+(

n−1)575 = (

n−1)5(

n−1) = 15n= 16The 16th term of this A.P is 78.