if an a.p an= 3n+2 find 12 th term
Answers
Answer:
Step-by-step explanation:
ANSWER
Given A.P
3,8,13,...…..,2533,8,13,...…..,253
first term of this A.P a_{1}=3a
1
=3
second term of this A.P a_{2}=8a
2
=8
common difference d=a_{2}-a_{1}=8-3=5d=a
2
−a
1
=8−3=5
the nth term of an A.P is given by
a_{n}=a_{1}+(n-1)da
n
=a
1
+(n−1)d
a_{n}=3+(n-1)5a
n
=3+(n−1)5
a_{n}=3+5n-5a
n
=3+5n−5
a_{n}=-2+5n …..eq(1)a
n
=−2+5n…..eq(1)
first calculate number of terms(n) in this A.P
put a_{n}=253a
n
=253 the last term of A.P in above eq(1)
253=-2+5n253=−2+5n
5n=253+25n=253+2
n=\dfrac{255}{5}n=
5
255
\implies n=51⟹n=51
hence this A.P contains 5151terms
for calculating 1212th term from the end means (51-11)(51−11)th term from starting of A.P
hence we have to calculate 40th term of this A.P
so put n=40n=40 in eq(1)
a_{40}=-2+5\times 40a
40
=−2+5×40
a_{40}=-2+200a
40
=−2+200
a_{40}=198a
40
=198
hence 1212th term of from the end of this A.P is 198198