Question

the sum first 5 terms and 9 terms of an ap is 72 and the first 7th and 12 terms is 97 find the ap
​

Answer 1

Answer:

6,11,16,21.....

Step-by-step explanation:

a5+a9=72

a+4d+a+8d=72

2a+12d=72.....1

a7+a12=97

2a+17d=97.....2

solving both the equations.....

we get, a=6 & d=5

therefore.....6,11,16,21......is the AP

Answer 2

Given :

• the sum(sn) of first 5 terms and 9 terms of ap is 72 and the of the first 7th and 12th term is 97

To find :

• AP

Solution :

We are given that,

a_5+ a_9 = 72

'.a + 4d +a + 8d = 72

2a + 12d = 72..(I)

and a_7 +a_12 = 97

2a + 17d = 97 ..(ii)

on equating (i) and (ii), we get

5d = 25

d = 5

put d = 5 in eq. (i)

2a + 12(5) = 72

2a + 60 = 72

2a = 72 - 60

2a = 12

a = 6

then,

a_1 6,a_2 11, a_3 = 16, a_4 = 21,. so on

AP is 6, 11, 16, 21,..