Question

if 10th term of an AP is 52 and 17th term is 20 more than 13th term,find the ap​

Answer 1

Step-by-step explanation:

it's so simple...hope you guys understand it

Answer 2

GIVEN :-

• $\sf 10^{th}$ term of the AP = 52

• $\sf 17^{th}$ term is 20 more than $\sf 13^{th}$ term .

TO FIND :-

• AP

SOLUTION :-

      $\boxed{\bf a_n = a+(n-1)d}$

 $\bullet \sf \ a_{10} = 52$

   $\longrightarrow \sf a+(10-1)d = 52 \\\\\longrightarrow a+9d = 52 \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ ....................(1)$

 $\bullet \sf \ a_{17} = a_{13} + 20$

   $\sf\longrightarrow a + (17-1)d = a+(13-1)d + 20 \\\\\longrightarrow a+16d =a+12d +20 \\\\\longrightarrow 16d-12d = 20\\\\\longrightarrow 4d = 20\\\\\longrightarrow d = 5$

  Substitute d = 5 in equation (1) ,

  $\longrightarrow\sf a+ 9\times 5 = 52 \\\\\longrightarrow a+45 = 52 \\\\\longrightarrow a = 7$

 $\bullet \sf \ a_1=7 \\\\\bullet a_2 = 7+5 = 12 \\\\\bullet \ a_3 = 12+5 = 17 \\\\\bullet \ a_4 = 17+5 = 22$

AP = 7 , 12 , 17 , 22 , ....................