Question

the 7 th team of AP is 20 and it's 13 th team is 32. find the AP​

Answer 1

GIVEN :-

• $7^{th}$ term of the AP = 20

• $13^{th}$ term of the AP = 32

TO FIND :-

• AP

SOLUTION :-

Let,

First term = a

Common difference = d

We know that,

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

$\bullet\sf \ a_7=20$

 $\longrightarrow\sf a+(7-1)d= 20 \\\\\longrightarrow a+6d = 20 \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ .................(1)$

$\bullet\sf \ a_{13}= 32$

 $\longrightarrow\sf a+(13-1)d= 32 \\\\\longrightarrow a+12d = 32 \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ .................(2)$

Equation(2) - Equation(1),

$\longrightarrow \sf 6d = 12\\\\\longrightarrow \bf d = 2$

Substitute the value of d in equation (1),

$\longrightarrow \sf a+6\times 2 = 20 \\\\\longrightarrow a+12= 20 \\\\\longrightarrow\bf a = 8$

First term = 8

Common difference = 2

$\bullet\sf \ a_1= 8 \\\\\bullet \ a_2= 8+2 = 10 \\\\\bullet a_3 = 10+2= 12 \\\\\bullet a_4 = 12+2= 14$

AP = 8 , 10 , 12 , 14 , .............