The first term of an A. P is -8.the ratio of the 7th term to the 9th term is 5:8.calculate the numbers

The 7th term is 10 and the 9th term is 16

(and the common difference d = 3)

Step-by-step explanation:

If by calculate the numbers, you mean the 7th term and 9th term, first, you will determine the common difference.

The nth term of an A.P is given by the formula

Tₙ= a+(n-1)d

Where Tₙ is the nth term

a is the first term

and d is the common difference

From the question,

a = -8

T₇ : T₉ = 5:8

From the formula

T₇ = a + (7-1)d = a + 6d

and T₉ = a + (9-1)d = a + 8d

Then.

a + 6d : a + 8d = 5:8

But a = -8

∴ -8 + 6d : -8 + 8d = 5:8

We can write that

(-8 + 6d) / (-8 + 8d) = 5/8

Cross multiply

8(-8+6d) = 5(-8+8d)

-64 + 48d = -40 + 40d

48d - 40d = -40 + 64

8d = 24

d = 24/8

d = 3

∴ The common difference is 3

Now, for the 7th term

From

T₇ = a + 6d

T₇ = -8 + 6(3)

T₇ = -8 + 18

T₇ = 10

and for the 9th term

T₉ = a + 8d

T₉ = -8 + 8(3)

T₉ = -8 + 24

T₉ = 16

Hence, the 7th term is 10 and the 9th term is 16

n=9

step-by-step explanation:

7 times a number = 7n

decreased by 13 = 7n-13

same as is =

5 times the number = 5n

increased by 5 = 5n+5

7n-13 = 5n+5

2n=18

n=9

my guess would be b and d, but i didn’t actually get out the pen and paper. lol