Question

(15 Points) Indicate the general rule for the arithmetic sequence with a3 = -4 and a8 = -29.

Answer 1

General rule » -5n+11

Explanation:

a3 = a+2d = -4 .......(1)

a8=a+7d = -29..........(2)

(2)-(1) » 5d= -25

d = -25/5

. = -5

substitute d = -5 in ( 1)

» a-2×-5= -4

a-10 = -4

a = -4 +10

= 6

General rule » a +(n-1)d

» 6 +(n-1)×-5

» 6-5n+5

» -5n+11

Answer 2

Explanation:

`a_3` = - 4

`a_3` = a* + (3- 1) d*

- 4 = a + 2d . . . . . . . . .(i)

`a_8` = - 29

`a_8` = a + ( 8 - 1) d

- 29 = a + 7d . . . . . . . . (ii)

subtracting equations (i) and (ii)

25 = 5d

d = -5

placing d = -5 in equation (i)

a - 10 = -4

a = 6

For an arithmetic Progtession

`a_n` = a + (n - 1)d

`a_n` = 6 + (n- 1)-5

`a_n` = 6 - 5n + 5

`\underline {a_n = 11 - 5n }`

`\\`

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`\boxed{ \mathfrak { a \:stands\: for\: first\: term } }`

*
`\boxed{ \mathfrak { d \:stands\: for\: common \: difference } }`