Question

Which term of the AP 3,15,27,39,...will be 120 more than its 21st term?

Answer 1

Hi Sis !!! 

Here is the answer of your query.

Given AP :- 3, 15, 27, 39, .......... 

Here, a = 3. 

d = 15-3 = 12.

 First. we will obtain the 21st term.  

By using formula, an = a + (n -1)d

a21 = 3 + (21 -1)12

= 3 + 20 × 12

= 3 + 240

= 243.

Hence, the 21st term of the AP is 243. 

Now, term that is 120 more than 21st term will be 

--> a21 + 120

--> 243 + 120

--> 363.

an = 363.  

Now, using formula

an = a + (n -1) d

363 = 3 + (n- 1) 12

360 = 12 (n -1)

n- 1 = 360/12

n -1 = 30

n = 31.

Hence, 31st term of the AP will be 120 more than 21st term of AP.

COMPLETED :::::

a31 - a21 

(3 + 30 × 12) - (3 +20 ×12)

= 363 - 243 = 120.

Hence, verified.

Hope it helps.

Answer 2

Answer:

Step-by-step explanation:

Here is the answer of your query.

Given AP :- 3, 15, 27, 39, ..........  

Here, a = 3.  

d = 15-3 = 12.

First. we will obtain the 21st term.  

By using formula, an = a + (n -1)d

a21 = 3 + (21 -1)12

= 3 + 20 × 12

= 3 + 240

= 243.

Hence, the 21st term of the AP is 243.  

Now, term that is 120 more than 21st term will be  

--> a21 + 120

--> 243 + 120

--> 363.

an = 363.  

Now, using formula

an = a + (n -1) d

363 = 3 + (n- 1) 12

360 = 12 (n -1)

n- 1 = 360/12

n -1 = 30

n = 31.

Hence, 31st term of the AP will be 120 more than 21st term of AP.

COMPLETED :::::

a31 - a21  

(3 + 30 × 12) - (3 +20 ×12)

= 363 - 243 = 120.

Hence, verified.

Hope it helps.