All categories

2 years ago

The 6th term of an arithmetic progression is 35 and the 13th term is 77. find the 1st term

Mathematics

1 answer:

GenaCL600 [577]2 years ago

8 0

Answer:

Step-by-step explanation:

The 6th term of an arithmetic progression is 35 and the 13th term is 77. find the 1st term

We know we have an arithmetic sequence.

a_n = (n - 1)*d + a_1

given:

a_6 = 35 = (6-1)*d + a_1

a_13 = (13 -1)*d + a_1 = 77

find a_1

we have 35 = 5d + a_1

and 77 = 12d + a_1

2 equations in 2 unknowns.

We can solve this.

77 = 12d + a_1

35 = 5d + a_1

minus the 2 equations from each other.

77 - 35 = 12d - 5d + a_1 - a_1

42 = 7d

d = 6

Find a_1

35 = 5*6 + a_1

35 = 30 + a_1

a_1 = 35 -30 = 5

a_1 = 5

You might be interested in

Answer problem below

garri49 [273]

Answer:

A = 2, B = 1, C = 28

Step-by-step explanation:

Find the slope of the line AB.

The slope:

m = (11 - 9)/(11 - 7) = 2/4 = 1/2

Since the altitude is perpendicular to AB, it has a slope of -2.

The line with the slope of -2 and passes through point C(6, 16).

Use point-slope equation to find the line:

y - 16 = -2(x - 6)
y - 16 = -2x + 12
y + 2x = 16 + 12
2x + y = 28

A = 2, B = 1, C = 28

7 0

3 years ago

Read 2 more answers

Answe these two, please show your work

I am Lyosha [343]

8+5x(-4)-(-6+-2)

13 x -4 - -6+-2

-52 - -6 + -2

58 + -2

-56

5 0

2 years ago

Read 2 more answers

Ms. Crest surveyed her class and found that 15 out of

Drupady [299]

15/30 brushed their teeth more than twice a day.
Fraction 1/2 <- (Simply by dividing by HCF)

Percentage= 50% (15 divided by 30 multiplied by 100) or you realise the 15 is half of 30. A half is 50%

Decimal= 0.5 (50% divided by 100)

5 0

2 years ago

PLZ, help me with this question.

GenaCL600 [577]

Answer:

The first one

Step-by-step explanation:

7 0

3 years ago

Read 2 more answers

Solve for a. a^2=-3a+88

Sergio [31]

Answer:

$a=8,-11$

Step-by-step explanation:

$a^2=-3a+88$

$a^2+3a=88$

$a^2+3a-88=0$

$x=\frac{-b\pm\sqrt{b^2-4ac} }{2a}$

$x=\frac{-3\pm\sqrt{3^2-4(1)(-88)} }{2(1)}$

$x=\frac{-3\pm\sqrt{9+352} }{2}$

$x=\frac{-3\pm\sqrt{361} }{2}$

$x=\frac{-3\pm19 }{2}$

$x=-11$ and $x=8$

Therefore, the values of $a$ are 8 and -11.

5 0

2 years ago