Question

an A.P. if the 4th term is 9, common difference is 2, 3rd term is

A) 2

B) 3

C) 5

) D) 7​

Answer 1

Answer:

$\fcolorbox{red}{white}{\huge \cal \green{D) 7}}$

Step-by-step explanation:

We know the formula for nth term in an A.P.

$\fcolorbox{red}{black}{ \bf{tn = a + (n - 1)d}}$

Where, tn = nth term, a = first term, n= no. of terms and d = common difference.

Here,

Given :

t4 = 9 and d=2 and

we have to find t3.

As per the formula,

$\bf \: t4 = a + (4 - 1) \times 2$

$\blue{ \bf \: t4 = a + 6} \: \: \: \: \: \: ...(1)$

Its value is given as 9, thus,

$\bf \: 9 = a + 6$

$\orange{ \bf \: a = 3}$

Also,

$\bf \: t3 = a + (3 - 1) \times 2$

$\blue{ \bf \: t3 = a + 4} \: \: \: \: \: \: ...(2)$

Substituting a=3, we get,

$\bf{t3 = 3 + 4}$

$\bold{ \fcolorbox{pink}{blue}{ \bf \: t3 = 7}}$

Answer 2

Answer:

The third term is equal to 7 for given arithmetic progression.

Therefore, the option (D) is correct.

Step-by-step explanation:

We have given for an arithmetic progression:

The value of fourth term, t₄ = 9

The common difference, d = 2

We can use the formula of nth term to find the 3rd term:

tₙ = a + (n-1)×d                                                   ....................(1)

Put n=4, d=2 and tₙ=9 in equation (1):

⇒   9 = a + (4-1)×2

⇒   9 = a + 6

⇒   a = 9-6

⇒   a = 3

Therefore, the first term = 3,

Put  n=3, a=3 and d=2 in equation (1);

t₃ = a + (n-1)×d

t₃ = 3 + (3-1)×2

t₃ = 3 + 4

t₃ = 7

Therefore, the third term is 7.