An important and exam oriented question from arithmetic progression chapter as it was already asked in previous year paper of 2014 in which we have been asked to find the nth term of the AP whose 7th term is -1 and 16th is 17.
RS Aggarwal, Class 10, Arithmetic Progression, chapter 5A, question no 31
Let a be the first term and d be the common difference of the given A.P.
Let the A.P. be a1,a2,a3,...,an,...
It is given that
a7=−1 and a16=17
⟹a+(7−1)d=−1 and a+(16−1)d=17
⟹a+6d=−1 …(i)
and, a+15d=17 …(ii)
Subtracting equation (i) from equation (ii), we get
9d=18
⟹d=2
Putting d=2 in equation (i), we get
a+12=−1
⟹a=13
Hence, General term =an=a+(n−1)d=−13+(n−1)×2=2n−15