Question

What is the initial term a and the common difference d of an arithmetic progression whose 4" term is 9 and the 8
term is 21?
Initial term =
Common difference =​

Answer 1

$\mathtt{\huge{ \fbox{Solution :)}}}$

Given ,

The fourth term and eighth term of an AP are 9 and 21

Let ,

The first term and common difference of AP be a and d

Thus ,

a + 3d = 9 ---- (i)

And

a + 7d = 21 ---- (ii)

Subtract eq (i) from eq (ii) , we get

(a + 7d) - (a + 3d) = 21 - 9

7d - 3d = 12

4d = 12

d = 12/4

d = 3

Put the value of d = 3 in eq (i) , we get

a + 3(3) = 9

a + 9 = 9

a = 0

Hence , the first term and common difference of AP are 0 and 3

Answer 2

$\large\underline\mathbb\red{CORRECT \:QUESTION:-}$

What is the initial term a and the common difference d of an arithmetic progression whose 4th term is 9 and the 8th

term is 21?

$\huge\underline\mathbb\red{GIVEN:-}$

• 4th term of AP = 9
• 8th term of AP = 21

$\huge\underline\mathbb\red{TO\:FIND:-}$

Find the initial term(a) and common difference (d) = ?

$\huge\underline\mathbb\red{SOLUTION:-}$

We have,

• 4th term = 9
• 8th term = 21

Let a be the first term and d be the common difference of an AP

According to question :-

$\implies$$\bf\blue{ a + 3d = 9 ......1)}$

$\implies$ $\bf\blue{a + 7d = 21.....2)}$

Taking equation 1)....

$\implies$ $\rm{a + 3d = 9}$

$\implies$ $\rm\red{a = 9 - 3d}$

put the value of a in equation 2)

$\implies$$\rm{ a + 7d = 21}$

$\implies$$\rm{(9 - 3d) + 7d = 21}$

$\implies$ $\rm{9 - 3d + 7d = 21}$

$\implies$$\rm{ 4d = 21-9}$

$\implies$$\rm{ 4d = 12}$

$\implies$ $\rm{d = \frac{12}{4}}$

$\implies$ $\large{\boxed{\bf{\green{d = 3}}}}$

put the value of 'd' in equation 1)

$\implies$ $\rm{a + 3 \times3 = 9}$

$\implies$ $\rm{a + 9 = 9}$

$\implies$ $\rm{a = 9-9 }$

$\implies$ $\large{\boxed{\bf{\green{a = 0}}}}$

Thus,

$\large{\boxed{\bf{ Common\: difference = 3}}}$

$\large{\boxed{\bf{Initial\: term = 0}}}$