Math, asked by elyasaasim, 9 months ago

if an a.p an= 3n+2 find 12 th term​

Answers

Answered by Knightbill81
0

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

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