Question

the 7 and 9 term of an ap are 13 and 21 find 8 and 10 term
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Answer 1

Correct question :

The 7th and 9th terms of an A.P are 13 and 21. Find 8th and 10th terms.

Solution :

$\boxed{ \boxed{\tt \large T_n = a+(n-1)d} } \\ \\ \tt where : \\ \\ \tt \bull T_n = n_{th} \: term \\ \\ \tt \bull n = number \: of \: terms \\ \\ \tt \bull a= first \: term \\ \\ \tt \bull d = common \: difference$

$\tt \: 7rd \: term : \\ \\ \tt \longrightarrow a + (7-1)d = 13 \\ \\ \tt \longrightarrow a + 6d = 13\\ \\ \tt \longrightarrow a = 13 - 6d ....(1)\\ \\ \tt9th \: term : \\ \\ \tt \longrightarrow a + ( 9-1)d = 21 \\ \\ \tt \longrightarrow a + 8d= 21\\ \\ \tt \longrightarrow a = 21 - 8d..........(2) \\ \\ \rm \: from \: (1) \: and \: (2) \: : \: \\ \\ \rm \rightarrow13 - 6d = 21 - 8d \\ \\ \rm \rightarrow 8d- 6d = 21 - 13\\ \\ \rm \rightarrow 2d =8\\ \\ \rm \rightarrow d = \dfrac{8}{2} \\ \\ \rm \rightarrow d = 4 \\ \\ \rm\rightarrow a = 21 - 8d\\ \rm\rightarrow a = 21 -( 8 \times 4) \\ \rm\rightarrow a = 21 -32\\ \rm\rightarrow a = - 11$

Therefore, d = 4 and a = -11

Now we have to find out 8th and 10th term.

8th term = a + (8-1) (d)

=> 8th term = -11 + (7×4)

=> 8th term = -11 + 28

=> 8th term = 17

10th term = a + (10-1) (d)

=>10th term = -11 + (9×4)

=>10th term = -11 + 36

=>10th term = 25

Answer :

8th term = 17 and 10th term = 25