Question

1. If the 9th and 21st terms of an A.P. are 75 and 183
respectively, find its 81st term.
(HOTS)​

Answer 1

Required Answer:-

Given:

• 9th term (a9) = 75
• 21st term (a21) = 183

Now,

By nth term formula,

•$\boxed{\rm{\large{a_n = a + (n - 1)d}}}$

Where, an, a, n and d are the last term, first term, term number and common difference respectively.

Then,

• a + 8d = 75 ------(1)
• a + 20d = 183 ------(2)

Subtracting (1) from (2),

➛ a + 20d - (a + 8d) = 183 - 75

➛ a + 20d - a - 8d = 108

➛ 12d = 108

➛ d = 9

Then, a = 75 - 72 = 3

To FinD:

• The 81st term of the AP.

Again by using nth term formula,

= a + (81 - 1)d

= a + 80d

= 3 + 80 × 9

= 3 + 720

= 723

Hence:

The required 81st term of the AP is 723 (Ans)

Answer 2

Answer:

723

Step-by-step explanation:

9th term = a + 8d = 75

21st term = a+20d = 183

                       -12d = -108

                     =>   d = 108/12

                     => d = 9

we have a+8d = 75

          =>  a + 8(9) = 75

          =>       a = 75-72

          =>       a = 3

so, 81st term = a+80d

                      = 3 +  80(9)

                      = 3 + 720

                      = 723