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lilavasa [31]
3 years ago
12

Find t12 term in an arithmetic progression having t3 = 10 and t10 = −4 .

Mathematics
1 answer:
Marat540 [252]3 years ago
6 0

Answer:

t12= -8

Step-by-step explanation:

t3

a+2d=10 (1)

t10

a+9d=-4. (2)

From (1)

a=10-2d. (3)

Sub into (3) into equ (2)

a+9d=-4

10-2d+9d=-4

10+7d=-4

7d=-4-10

7d=-14

Divide both sides by 7

d=-14/7

d= -2

10=a+2d

10=a+2(-2)

10=a-4

10+4=a

14=a

a=14

t12=a+11d

= 14+11(-2)

=14-22

= -8

t12= -8

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Step-by-step explanation:

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(

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Simplify  

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Multiply the exponents in  

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n

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Apply the power rule and multiply exponents,  

(

a

m)n

=

a

m

n

.

n

1

2

⋅

2

=

(

18

√

8

−

8

√

18

)

2

Cancel the common factor of  2  

Cancel the common factor.

n

1

2

⋅

2

=

(

18

√

8

−

8

√

18

)

2

Rewrite the expression.

n

1

=

(

18

√

8

−

8

√

18

)

2

Simplify.

n

=

(

18

√

8

−

8

√

18

)

2

Simplify  

(

18

√

8

−

8

√

18

)

2

Simplify each term.

Rewrite  

8  as  2

2

⋅

2

.  

Factor  

4  out of  8  

n

=

(

18

√

4

(

2

)

−

8

√

18

)

2

Rewrite  

4  as  2

2  

n

=

(

18√

2

2

2

−

8

√

18

)

2

Pull terms out from under the radical.

n

=

(

18

(

2

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2

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−

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√

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2

Multiply  

2  by  18  

n

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(

36

√

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−

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√

18

)

2

Rewrite  

18

as  

3

2

⋅

2

.

Factor  

9

out of  

18

.

n

=

(

36

√

2

−

8

√

9

(

2

)

)

2

Rewrite  

9

as  

3

2

.

n

=

(

36

√

2

−

8

√

3

2

⋅

2

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2

Pull terms out from under the radical.

n

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36

√

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8

(

3

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2

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(

36

√

2

−

24

√

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2

Simplify terms.

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12

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Simplify the expression.

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12

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2

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n

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12

2

√

2

2

Raise  

12

to the power of  

2

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n

=

144

√

2

2

Rewrite  

√

2

2

as  

2

.

Use  

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x

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a

x

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√

2

as  

2

1

2

.

n

=

144

(

2

1

2

)

2

Apply the power rule and multiply exponents,  

(

a

m

)

n

=

a

m

n

.

n

=

144

⋅

2

1

2

⋅

2

Combine  

1

2

and  

2

.

n

=

144

⋅

2

2

2

Cancel the common factor of  

2

.

Cancel the common factor.

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144

⋅

2

2

2

Rewrite the expression.

n

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144

⋅

2

1

Evaluate the exponent.

n

=

144

⋅

2

Multiply  

144

by  

2

.

n

=

288

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