Question

the 8th term of ap is 17 and its 14th term is 29 the common difference of ap is​

Answer 1

Answer:

The common difference of ap is​ 2

Step-by-step explanation:

Answer 2

Given :

$\sf \bullet \: a_{8} = 17 \\ \sf \bullet \: a_{14} = 29$

To find : Common difference (d)

Formula used :

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

Here ,

• a = 1st term
• d = common difference

$\sf \bullet \: a_{n} = n^{th} \: term$

Solution :

$\sf \implies \: \: a_{8} = a \: + \: (8 - 1)d \\ \sf \implies \: \: 17 = a \: + \: 7d \: \: \: ...........equation \: 1$

$\sf \implies \: a_{14} = a \: + \: (14 - 1)d \\ \sf \implies \: 29 = a \: + \: 13d \\ \sf \implies \: a = 29 \: - \: 13d$

Putting value of a , in equation 1 , we get;

$\sf \implies \: 17 = (29 - 13d) + 7d \\\\ \sf \implies \: 17 = 29 - 6d \\ \\ \sf \implies \: 29 - 17 = 6d \\\\ \sf \implies \: 12 = 6d \\\\ \sf \implies \: d = \dfrac{12}{2} \\ \\ \sf \implies \: \bold {d \: = 2}$

ANSWER : Common difference (d) = 2