Question

Find the first, fourth, and tenth terms of the arithmetic sequence described by the given rule.
A n=1+(n-1)(-5.7)

Answer 1

Answer:

First term is 1 , fourth term is - 16.1 and 10th term is - 50.3.

Step-by-step explanation:

Given,

nth term of this arithmetic progression is 1 + ( n - 1 )( - 5.7 ), where n describes the number of terms.

Here,

If we have to find the first term, value of n should be substituted as equal to 1.

Thus,

= > First term = a$_1$=1 + ( 1 - 1 )( - 5.7 )

= > First term = a$_1$= 1 + 0

= > First term = a$_1$= 1

Then,

If we have to find the first term, value of n should be substituted as equal to 1.

Thus,

= > Fourth term = 1 + ( 4 - 1 )( - 5.7 )

= > Fourth term = 1 + 3( - 5.7 )

= > Fourth term = 1 - 17.1

= > Fourth term = - 16.1

Similarly,

= > 10th term = 1 + ( 10 - 1 )( - 5.7 )

= > 10th term = 1 + 9( -5.7 )

= > 10th term = 1 - 51.3

= > 10th term = - 50.3

Hence, first term is 1 , fourth term is - 16.1 and 10th term is - 50.3.

Answer 2

$a_{n}$ = a + (n - 1)d

$a_{n}$ = 1 + (n - 1) (-5.7)

Means...

First term (a) = 1

Common difference (d) = - 5.7

___________ [GIVEN]

• We have to find the first, fourth and tenth term of the AP.

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Now...

$a_{n}$ = a + (n - 1)d

• For first term

$a_{1}$ = 1 + (1 - 1) (-5.7)

$a_{1}$ = 1 + (0) (-5.7)

$a_{1}$ = 1 + 0 = 0

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• For fourth term

$a_{4}$ = 1 + (4 - 1) (-5.7)

$a_{4}$ = 1 + (3) (-5.7)

$a_{4}$ = 1 + (-17.1)

$a_{4}$ = - 16.1

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• For tenth term

$a_{10}$ = 1 + (10 - 1) (-5.7)

$a_{10}$ = 1 + (9) (-5.7)

$a_{10}$ = 1 + (-51.3)

$a_{10}$ = - 50.3

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First term is 1, forth term is - 16.1 and tenth term is - 50.3

____________ [ANSWER]

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