Question

Write the next four terms of an A.P. whose first term is 11 and the common difference 2.​

Answer 1

Answer:

11,13,15,17

Step-by-step explanation:

reffer to picture for detailed solution

Answer 2

$\huge{\sf{\underline{\underline{AnSwEr:-}}}}$

$\large{\sf{\underline{\underline{SoluTion:-}}}}$

$\large\sf\therefore\green{NexT \: Terms\: =13,15,17,19}$

$\large{\sf{\underline{\underline{Given:-}}}}$

$\bullet$ $\rm\ First \: Term(a_1) = 11$

$\bullet$ $\rm\ Common \: difference(d) =2$

$\large{\sf{\underline{\underline{To \: FinD :-}}}}$

$\bullet$$\rm\ Next \: FouR \: terms$

$\large{\sf{\underline{\underline{STep \: bY \: STep \: expLanaTion :-}}}}$

$\large\sf\therefore\purple{Method \: 1: }$

We know that general form of AP is ;

$\large\red{\boxed{\sf A.P = a,a+d,a+2d,a+3d...}}$

Now,

_________________

Four next terms after the first will be ;

$\large\sf\to\ a+d,a+2d,a+3d,a+4d \\ \\ \large\sf\to\ (11+2), (11+2 \times\ 2), (11+3 \times\ 2) , (11+4 \times\ 2 )\\ \\ \large\sf\to\ 13,15,17,19$

____________________

$\large\sf\therefore\purple{Method \: 2:}$

Formula used here ;

$\large\red{\boxed{\sf a_n= a+(n-1)d }}$

Now,

We have to find four terms after the first term$\sf\ (a_1)$So ,the next terms will be $\sf\ a_2,a_3,a_4,a_5$....

$\large\tt\ LeT's \: begin !$

_______________

$\bullet$$\large\tt\ a_2 = 11+(2-1)2$

$\large\tt\to\ a_2=11+ (1)2$

$\large\tt\to\ a_2 =13$

_____________

$\bullet$$\large\tt\ a_3= 11+(3-1)2$

$\large\tt\to\ a_3= 11+(2)2$

$\large\tt\to\ a_3=15$

____________

$\bullet$$\large\tt\ a_4 =11+(4-1)2$

$\large\tt\to\ a_4= 11+(3)2$

$\large\tt\to\ a_4 =17$

_____________

$\bullet$$\large\tt\ a_5= 11+(5-1)2$

$\large\tt\to\ a_5= 11+(4)2$

$\large\tt\to\ a_5= 19$

•°•Now, The AP is ;

$\large\sf\to\ 11,13,15,17,19....$

•°•Next four terms after first term are ;

$\large\sf\to\ 13,15,17,19$