Question

An arithmetic sequence has it's 5th term to equal 22 and it's 15th term Equal 62 find it's 102nd term

Answer 1

Answer:

410

Step-by-step explanation:

Since we know that,

• aₙ = a + (n - 1)d

→ 5th Term = 22

→ a + 4d = 22 ___(1)

→ 15th term = 62

→ a + 14d = 62 ___(2)

On doing (2) - (1) we get,

→ 10d = 40

→ d = 4

Hence, a = 62 - 14d

→ a = 62 - 14(4) = 6

So, 102nd term = a + 101d

→ 6 + 101(4)

→ 6 + 404 = 410

[Note :-

• 22 = a + (n - 1)d
• 22 = a + (5 - 1)d
• 22 = a + 4d]

Answer 2

Solution :-

Formula used : aₙ = a + (n - 1)d

Case I : An arithmetic sequence has it's 5th term to equal 22.

=> 22 = a + (5 - 1)d

=> a = 22 - 4d _____(i)

Case II : it's 15th term equal 62.

=> 62 = a + (15 - 1)d

=> 62 = 22 - 4d + 14d [from equation (i)]

=> 10d = 40

=> d = 40/10 = 4

Putting the value of d in equation (i) we get,

=> a = 22 - 4 × 4

=> a = 22 - 16 = 6

Now,

It's 102nd term = 6 + (102 - 1)4

= 6 + (101)4

= 6 + 404 = 410

Hence,

It's 102nd term = 410