In this question the last term of A.P. is given, you have to find which term of A.P. this must be. This is question number 4 exercise 5.2,NCERT Maths solutions.
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Solution:
11th term, a11 = 38
and 16th term, a16 = 73
We know ,
an = a + (n−1)d
a11 = a + (11−1)d
38 = a + 10d ………………………………. (i)
By the same way,
a16 = a +(16−1)d
73 = a+15d ………………………………………… (ii)
On subtracting eq. (i) from (ii),
35 = 5d
d = 7
From eq. (i),
38 = a+10×(7)
38 − 70 = a
a = −32
a31 = a +(31−1) d
= − 32 + 30 (7)
= − 32 + 210
= 178
So, 31st term is 178.