Question

which term of the ap 3,15,27,39 will be 120 more than its 21 term​

Answer 1

Here is the answer to your question:

Answer 2

✬ 31st Term ✬

Step-by-step explanation:

Given:

• AP series is 3 , 15 , 27 , 39

To Find:

• Which term of AP will be 120 more than its 21st term.

Solution: Here in this AP series we have

• a = First term = 3
• d = common difference = 15 – 3 = 12

As we know that nth term of AP is given by

★ a²¹ = a + (n – 1)d ★

$\implies{\rm }$ a²¹ = 3 + (21 – 1)12

$\implies{\rm }$ a²¹ = 3 + 20(12)

$\implies{\rm }$ a²¹ = 3 + 240

$\implies{\rm }$ a²¹ = 243

Now, 120 more than a²¹ will be

• 243 + 120 = 363

Let nth term of AP will be 120 more than 21st term therefore,

➬ aⁿ = a + (n – 1)d

➬ 363 = 3 + (n – 1)12

➬ 363 = 3 + 12n – 12

➬ 363 = – 9 + 12n

➬ 363 + 9 = 12n

➬ 372 = 12n

➬ 372/12 = n

➬ 31 = n

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