Question

the 17th term of an AP is 7 more than the 10th term find the common difference d​

Answer 1

Answer:

$\sf\small{ \underline{\underline{ \pmb{Given:-}}}}$

• The 17th term of an AP is 7 more than the 10th term

$\sf\small{ \underline{\underline{ \pmb{To \: Find:-}}}}$

• Common difference

$\sf\small{ \underline{\underline{ \pmb{ Solution:-}}}}$

We know that, for an A.P series

• Formula we can use
• $\underline{ \boxed{ \purple{\sf \: a_n = a+(n−1)d}}} \pink \bigstar$

$\sf \implies a_{17} = a+(17−1)d$

$\sf \implies \: a_{17} = a +16d$

• In the same way,

$\sf \implies \: a_{10} = a+9d$

As it is given in the question,

$\sf \: a_{17} − a_{10 }= 7$

$\sf \implies \: (a +16d)−(a+9d) = 7$

$\sf \implies \: 7d = 7$

$\sf \implies \: d = \cancel \frac{7}{7}$

$\sf \implies \: d = 1$

Therefore, the common difference is 1.