Question

In an A.P., if $a = 8$ and $a_{10} = -19$, then value of $d$ is:

• A. $3$
• B. $-\frac{11}{9}$
• C. $-\frac{27}{10}$
• D. $-3$

Answer 1

Answer: (D)

$-3$

Answer 2

In an arithmetic progression (A.P.), the $n$-th term is given by the formula:

$a_n = a + (n - 1)d$

Where:

• $a_n$ is the $n$-th term,
• $a$ is the first term,
• $d$ is the common difference.

We are given:

• $a = 8$ (the first term),
• $a_{10} = -19$ (the 10th term),
• We need to find $d$ (the common difference).

Substitute the known values into the formula for the 10th term:

$a_{10} = a + (10 - 1)d \implies -19 = 8 + 9d$

Now, solve for $d$:

$-19 - 8 = 9d \implies -27 = 9d \implies d = -3$

Thus, the correct answer is:

$d)\ -3$