Question

if the sum of 5th and 9th term of A.P 72 and the sum of 7th and -12th term is 97 find A.P​

Answer 1

Answer:

31, 36,41,46,...

step by step explanation:

given,

t₅ + t₉ = 72 ---------(1)

t₇ + t₁₂ = 97-----------(2)

we have n'th term  = a + (n-1)d

(1) =>  a+4d + a+8d = 72  

   => 2a+12d = 72  ------------ (3)

(2) => a+6d + a+11d = 97  

   =>2a+17d = 97     ------------ (4)                                                  

(3)-(4) =>   2a+12d-2a-17d = 72-97

-5d  = -25

=>   d = 25/5

=>   d = 5

substitute d=5 in (1) , we get

2a+2d = 72

=>     2a + 2(5) = 72

=>     2a = 72-10

=>     2a = 62

=>     a = 62/2 = 31      

so, A.P is

                => 31, 31+5 , 31+2(5)  ,  31+3(5),..

                => 31, 36 , 31+10  ,  31+15,...

                => 31, 36,41,46,..

Answer 2

$\huge{\mathcal{\purple{A}\green{N}\pink{S}\blue{W}\purple{E}\green{R}\pink{!}}}!$

• 31,36,41,46 is the answer
• hope it will help you!!
• mark as brainleist!!