Question

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The 5th term of an arithmetic sequence is 17 and 17th term is 5. what is the 22nd term​

Answer 1

Answer:

0

Step-by-step explanation:

IN THIS QUESTION COMMON DIFFERENCE (D) = -1

22 THEM=A+21D

A=?

5 TH TERM=A+4D=17

          D=-1⇒A-4=17

           A=17+4

          A=21

22 TERM=A+21D

              =21+21×-1

               =21+-21

            =0

Answer 2

Answer:

The required 22nd term is 0.

Step-by-step explanation:

nth term of an A.P is given by,

$\bf a_n = a+(n-1) d$

where

a denotes the first term

d denotes the common difference.

5th term is 17 :

$\sf a_5 = a+(5-1)d$

17 = a + 4d

a = 17 - 4d --(1)

17th term is 5 :

$\sf a_{17} = a + (17-1)d$

5 = a + 16d

5 = 17 - 4d + 16d [since a = 17 - 4d]

5 = 17 + 12d

12d = 5 - 17

12d = -12

d = -12/12

d = -1

Therefore, common difference = -1

Substitute d = -1 in equation (1),

a = 17 - 4(-1)

a = 17 + 4

a = 21

First term = 21

We've to find the 22nd term.

$\sf a_{22} = a+(22-1)d \\ \sf a_{22}= 21 + 21(-1) \\ \sf a_{22} = 21 - 21 \\ \sf a_{22} = 0$

Therefore, 22nd term is 0.