Question

the 8th term of an A.P is 17 and 19th term is 39 find the common difference​

Answer 1

The common difference​ (d) = 2

Step-by-step explanation:

Let the first term = a and common difference = d

To find, the common difference​ (d) = ?

Using the formula,

The nth term of an AP

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

∴ The 8th term of an A.P

$a_{8}$ = a + (8 - 1)d

⇒ a + 7d = 17                                ................ (1)

The 19th term of an A.P

$a_{19}$ = a + (19 - 1)d

⇒ a + 18d = 39                             ................ (2)

Subtracting (1) from (2), we get

a + 18d - (a + 7d) = 39 - 17

⇒ a + 18d - a - 7d = 39 - 17

⇒ 11d = 22

⇒ d = $\dfrac{22}{11}$

⇒ d = 2

Thus, the common difference​ (d) = 2

Answer 2

Common difference = 2

Step-by-step explanation:

General term of the A.P is

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

8th term = 17

Substitute n = 8 in general term.

$a_8=a+(8-1)d$

$17=a+7d$ ---------- (1)

19th term = 39

Substitute n = 19 in general term.

$a_{19}=a+(19-1)d$

$39=a+18d$ ---------- (2)

(2) - (1) gives,

(a + 18d) - (a + 7d) = 39 - 17

a + 18d - a - 7d = 22

11d = 22

$d=\frac{22}{11}$

d = 2

Common difference = 2

To learn more...

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