Question

tenth term of the arithmetic sequence is 15 and fifteenth term is 10
a) what is the common difference b)what is the first term
c) what is the 25th term​

Answer 1

Answer:

a) 5

b) 25

c) 0

Step-by-step explanation:

hope this helps you

Answer 2

$\sf\huge\underline{Question:}$

a) what is the common difference

b)what is the first term

c) what is the 25th term

$\sf\huge\underline{Answer:}$

Given that, tenth term = 15 and fifteenth term = 10

→$a_{n} = a + (n - 1)d$

$a_{10} = a + (10- 1)d$

$a_{10} = a + 9d$

Let this be equation 1

$a_{n} = a + (n - 1)d$

$a_{15} = a + (15 - 1)d$

$a_{15} = a + 14d$

Let this be equation 2. Now by solving the equations we get the common difference

Common difference (d) = -1

→First term (a) can be found using the equation 2

$a = 10 - 14d = - 4$

First term of the AP = -4

→ $a_{n} = a + (n - 1)d$

$a_{25} = - 4 + (25 - 1)( - 1)$

$a_{25} = - 4 - 24 = - 28$

The 25th term of this AP is -28

Have a good night!