Question

Write the first four terms of the AP when the first term a and common difference d are (i) a = 10, d = 10 (ii) a = -2 , d = 0

Answer 1

Answer:

So here A.P full for is Arithmetic Progression

(i) a = 10 , d = 10

so here a that  is first term means 10

and d is the difference that is 10

now, we have to  make equation that is

a = 10

a1 = 10+10 = 20

a1 = 20

a2= 20+10 = 30

a2=30

a3=20+10

a3=30

a4=30+10

a4=40

so here your next three terms are 10,20,30,40

(ii) so here a that  is first term means -2

  and d is the difference that is 0

  a = -2

a1 = -2 + 0

a1 = -2

a2 = -2 +0

a2 = -2

a3 = -2 +0

a3 = -2

a4= -2 +0

a4 = -2

so here your next terms are -2,-2,-2,-2

there is no  decreasing or increasing order because the differnce is 0

Answer 2

(i) Given :-

• First term (a) = 10

• Common difference (d) = 10

To find :-

• The first four terms of the AP

Solution :-

we know that,

$\blue{\bigstar}\:\:{\underline{\boxed{\bf\red{a_1=a+0d}}}}$

$\rm\longrightarrow\:a_1=10+0\times\:d$

$\rm\longrightarrow\:a_1=10+0$

$\rm\longrightarrow\:a_1=10$

$\green{\bigstar}\:\:{\underline{\boxed{\bf\pink{a_2=a+d}}}}$

$\rm\longrightarrow\:a_2=10+10$

$\rm\longrightarrow\:a_2=20$

$\blue{\bigstar}\:\:{\underline{\boxed{\bf\purple{a_3=a+2d}}}}$

$\rm\longrightarrow\:a_3=10+2\times\:10$

$\rm\longrightarrow\:a_3=10+20$

$\rm\longrightarrow\:a_3=30$

$\pink{\bigstar}\:\:{\underline{\boxed{\bf\orange{a_4=a+3d}}}}$

$\rm\longrightarrow\:a_4=10+3\times\:10$

$\rm\longrightarrow\:a_4=10+30$

$\rm\longrightarrow\:a_4=40$

Hence,the first four terms of the AP will be 10,20,30,40.

(ii) Given :-

• first term (a) = -2

• Common difference (d) = 0

To find :-

• The first four terms of the AP

Solution :-

we know that,

$\purple{\bigstar}\:\:{\underline{\boxed{\bf\pink{a_1=a+0d}}}}$

$\rm\longrightarrow\:a_1=-2+0\times\:0$

$\rm\longrightarrow\:a_1=-2$

$\orange{\bigstar}\:\:{\underline{\boxed{\bf\green{a_2=a+d}}}}$

$\rm\longrightarrow\:a_2=-2+0$

$\rm\longrightarrow\:a_2=-2$

$\red{\bigstar}\:\:{\underline{\boxed{\bf\orange{a_3=a+2d}}}}$

$\rm\longrightarrow\:a_3=-2+2\times\:0$

$\rm\longrightarrow\:a_3=-2$

$\orange{\bigstar}\:\:{\underline{\boxed{\bf\blue{a_4=a+3d}}}}$

$\rm\longrightarrow\:a_4=-2+3\times\:0$

$\rm\longrightarrow\:a_4=-2$

Hence,the first four terms of the AP will be -2,-2,-2,-2.