Question

35] The first term of the 1" AP is 3 less than the first term of the 2nd AP. The 10th term of the 1st
AP is 49 and the 5th term of the 2nd AP is 27. Find the two APs if their common difference is
the same.
​

Answer 1

answer:

1st AP=4,9,14

2nd Ap=7,12,17

Answer 2

First A.P

4,9,14,...

Second A.P

7,12,17,22,27,..

Step-by-step explanation:

Let a and d be the first term and common difference of first A.P .

a' and d' be the first term and common difference of second A.P

Given: d=d'

According to question

$a=a'-3$

$a'=a+3$

$a_{10}=a+9d=49$...(1)

Using the formula of nth term of A.p

$a_n=a+(n-1)d$

Where a=First term

d=Common difference

n=Total number of terms

$a'_5=a'+4d'=27$

$a'+4d=27$

Substitute the values of a'

$a+3+4d=27$

$a+4d=27-3=24$

$a+4d=24$...(2)

Subtract equation (2) from equation (1)

$5d=25$

$d=\frac{25}{5}=5$

Substitute the values of d in equation (1)

$a+9(5)=49$

$a+45=49$

$a=49-45=4$

$a'=a+3=4+3=7$

$d'=d=5$

$a_2=a+d=4+5=9$

$a_3=a+2d=4+2(5)=4+10=14$

First A.P

4,9,14,...

$a'_2=a'+d'=7+5=12$

$a'_3=a'+2d'=7+2(5)=17$

Second A.P

7,12,17,22,27,..

#Learn more:

https://brainly.in/question/5031184:Answered  by Rohitkumargupta