Question

The sum of 3 no.s in an Ap is 30. The ratio of first term to the 3rd term is 3:7.find the number​

Answer 1

Answer: 6,10,14

Step-by-step explanation:

Let the three numbers in AP be:

(a-d) ,a,(a+d)

sum of no.=30 [Given]

=> (a-d)+a+(a-d) = 30

=> 3a =30

=> a=10

now,

Ratio of first no : third no. = 3:7 [Given]

=> (a-d) / (a+d) = 3/7

=> (10-d) / (10+d) =3/7                  [a=10]

=> 70-7d = 30+3d

=> 70-3- = 3d+7d

=> 40 = 10d

=> d=4

and a=10 [from above]

Thus, numbers are :

1st number = (a-d) = 10-4 = 6

2nd number = a = 10

3rd number = (a+d) = 10+4 = 14

Answer 2

${\bold{\underline{\underline{Answer:}}}}$

${\bold{\therefore A.P=6,10,14,....}}$

${\bold{\underline{\underline{Step-by-step\:explanation:}}}}$

• In the given question information given about the sum of 3 no.s in an Ap is 30. The ratio of first term to the 3rd term is 3:7.

• We have to find the number.

$\bold{Let \: First \: term = a }\\ \\ \bold{Common \: difference = d} \\ \\ \underline \bold{Given :} \\ \implies s_{3} = 30 \\ \\ \implies a : a_{3} = 3 : 7 \\ \\ \underline \bold{To \: Find :} \\ \implies A.P = ?$

• According to given question :

$\bold{For \: sum \: of \: 3 \: terms : } \\ \implies a + a + d + a + 2d = 30 \\ \\ \implies 3a + 3d = 30 \\ \\ \implies a + d = \frac{30}{3} \\ \\ \implies a = 10 - d - - - - - (1) \\ \\ \bold{for \: ratio : } \\ \implies \frac{a}{a + 2d} = \frac{3}{7} \\ \\ \implies 7a = 3a + 6d \\ \\ \implies 7a - 3a = 6d \\ \\ \implies 4a = 6d \\ \\ \bold{Putting \: value \: of \: a : } \\ \implies 4 \times (10 - d) = 6d \\ \\ \implies 40 - 4d = 6d \\ \\ \implies d = \frac{40}{10} \\ \\ \bold{\implies d = 4} \\ \\ \bold{Putting \: value \: of \: d \: in \: (1) : } \\ \implies a = 10 - d \\ \\ \implies a = 10 - 4 \\ \\ \bold{\implies a = 6} \\ \\ \bold{\therefore A.P = 6,10,14,...}$