Question

Which term of ap is 13,29,25.... , and 69,68,67 .... Is same also find that term?

Answer 1

Correct question:

Which term of ap is 13,19,25.... , and 69,68,67 .... Is same also find that term?

Answer:

equal term of both APs = 9

9th of the APs = 61

Step-by-step explanation:

given

AP = 13,29,25....

here,

first term(a) = 13

common difference (d) = 19 - 13

= 6

so,

nth term = a + (n - 1)d

= 13 + (n - 1)6

= 13 + 6n - 6

= 6n + 7. ...(1)

and another AP = 69,68,67...

here,

first term(a) = 69

common difference(d) = 68 - 69

= -1

so,

nth term = a + (n - 1)d

= 69 + (n - 1)(-1)

69 - n + 1

-n + 70. ....(2)

now,

to find,

nth term which is equal in both APs

so,

According to the question,

6n + 7 = -n + 70

6n + n = 70 - 7

7n = 63

n = 63/7

n = 9

so,

9th term of both APs will equal

now,

9 term

= -n + 70

-9 + 70

= 61

so,

equal term of both APs = 9th

9th of the APs = 61

Answer 2

Correct question:

Which term of AP is 13,19,25.... , and 69,68,67 .... Is same also find that term?

Answer:

equal term of APs = 9

9th of the APs = 61

Step-by-step explanation:

given

AP = 13,19,25....

a =13

d = 19 - 13 = 25 -19

= 6

now,

nth term = 13 + (n - 1)6

= 13 + 6n - 6

= 6n + 7 ...(1)

now,

AP = 69,68,67...

a = 69

d = 68 - 69 = 67 - 68

= -1

now,

nth term = 69 + (n - 1)(-1)

69 +(- n + 1)

69 - n + 1

-n + 70. ....(2)

now,

given,

nth term of both APs are equal

so,

6n + 7 = -n + 70

6n + n = 70 - 7

7n = 63

n = 63/7

n = 9

equal term of both APs = 9th

9th term = 6n + 7

= 6(9)+ 7

54 + 7

= 61

So,

equal term = 61