In an AP, the ratio of the 7th term to the 10th term is -1. If the 16th term is -15, what is the 3rd term?

The 3rd term is 11

Step-by-step explanation:

The given parameters for the Arithmetic Progression, AP, are;

The ratio of the 7th term to the 10th term = (a + 6·d)/(a + 9·d) = -1

The 16th term = -15 = a + 15·d

The 3rd term= a + 2·d

From the 7th to the 10th term ratio, we have;

a + 6·d = -a - 9·d

2·a = -15·d

-2·a = 15·d...(1)

From the 16th term of the AP, we have;

-15 = a + 15·d =  a + -2·a = -a

a = 15

From equation (1), -2·a = 15·d, we have;

-2·a = -2 × 15 = 15·d

15·d = -2 × 15

d = -2 × 15/15 = -2

d = -2

The 3rd term = a + 2·d = 15 + 2 × -2 = 11

∴ The 3rd term = 11

a variable is any characteristics, number, or quantity that can be measured or counted. a variable may also be called a data item. hope i !

exa:

)

3+11

14

step-by-step explanation:

from this example, we can see that subtracting with integers is the same as adding the opposite. we can solve using a number line or by using the saying "keep, change, change" to us solve. it is important to remember that we can subtract a negative and end up with a larger number than we started with.