The sum of the first two terms of an arimethic sequence is 15 and the sum of the next two terms is 43. Write the first 4 terms of the sequence?

Question

The sum of the first two terms of an arimethic sequence is 15 and the sum of the next two terms is 43. Write the first 4 terms of the sequence?

2 Answers

Impact of this question

7478 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2017-06-05T17:21:49

the terms are 4, 11, 18, 25

Explanation:

The first equation is: $n + n + x = 15$ $" "n + n + x = 15$

The second equation is: $n + 2 x + n + 3 x = 43 .$ $" " n + 2x + n + 3x = 43.$

$n$ $n$ is the first term $x$ $x$ is the variable of the sequence. so
$n + x$ $n + x" "$ is the second term
$n + 2 x$ $n + 2x" "$ is the third term
$n + 3 x$ $n + 3x" "$ is the fourth term.

Solving for x in terms of

$n + 2 x + n + 3 x = 43$ $n + 2x + n + 3x = 43 " "$ adding like terms.

$2 n + 5 x = 43$ $2n + 5x = 43" "$ subtracting $5 x$ $5x$ from both side sides gives

$2 n + 5 x - 5 x = 43 - 5 x$ $2n + 5x -5x = 43 -5x" "$ resulting in

$2 n = 43 - 5 x$ $2n = 43 -5x" "$ this can be substituted into the first equation.

$n + n + x = 15$ $n + n + x = 15" "$ which is the same as

$2 n + x = 15$ $2n + x = 15" "$ now substitute $2 n = 43 - 5 x$ $2n = 43 -5x$ into the question.

$43 - 5 x + x = 15$ $43 -5x + x = 15" "$ combine like terms

$43 - 4 x = 15$ $43 - 4x = 15$ add $4 x$ $4x$ to both sides and subtract $15$ $15$ from both sides

$43 - 15 - 4 x + 4 x = 15 - 15 + 4 x$ $43 -15 - 4x + 4x = 15-15 + 4x" "$ gives.

$28 = 4 x$ $28 = 4x " "$ Divide both sides by $4$ $4$ to solve for $x$ $x$

$\frac{28}{4} = \frac{4 x}{4}$ $28/4 = (4x)/4$ gives

$7 = x$ $7 = x " "$ This is the variable of the sequence.

Putting $7$ $7$ in for $x$ $x$ to solve for $n$ $n$ the first number in the sequence.

$n + n + 7 = 15$ $n + n + 7 = 15" "$ combine like terms

$2 n + 7 = 15$ $2n + 7 = 15" "$ subtract 7 from both sides

$2 n + 7 - 7 = 15 - 7$ $2n + 7 -7 = 15 -7 " "$ which gives

$2 n = 8$ $2n = 8 " "$ Divide both sides by 2

$\frac{2 n}{2} = \frac{8}{2}$ $(2n)/2 = 8/2$ gives

$n = 4$ $n = 4$ so $4$ $4$ is the first number of sequence add $7$ $7$

$n_{2} = 114 + 7 = 11$ $n_2 = 11" " 4 + 7 = 11$

$n_{3} = 1811 + 7 = 18$ $n_3 = 18" " 11 +7 = 18$

$n_{4} = 2518 + 7 = 25$ $n_4 = 25" "18 + 7 = 25$

Answer 2 · 2017-06-05T20:04:59

$4111825$ $4" "11" "18" "25$

Explanation:

The terms in an arithmetic sequence can be written in terms of the first term, $a$ $a$ and the common difference, $d$ $d$ .

$d$ $d$ is added to each term to get to the next.

Terms $(n)$ $(n)$ : $1 w w w w w 2 w w w w w w 3 w w w w w w 4$ $" "1color(white)(wwwww)2color(white)(wwwwww)3color(white)(wwwwww)4$

Values: $(T_{n}) a w w w (a + d) w w (a + 2 d) w w (a + 3 d))$ $(T_n)" "color(red)(a)color(white)(www)color(red)((a+d))color(white)(ww)color(blue)((a+2d))color(white)(ww)color(blue)((a+3d)))$

We know that the sum of $T_{1} and T_{2} = 15$ $color(red)(T_1 and T_2 = 15$
We know that the sum of $T_{3} and T_{4} = 43$ $color(blue)(T_ 3 and T_4 = 43)$

$:.color(red)( a+a+d = 15)color(white)(wwww.w)rarr color(red)(2a +d = 15)...........A$
$:. color(blue)(a+2d + a +3d = 43)" "rarr color(blue)(2a +5d = 43)..........B$

The difference between A and B will give us a value for $4d$

$B - A:color(white)(wwwww) 4d=28$
$color(white)(wwwwwnwwnww) d=7$

We now know that the terms differ by $7$ each time.

$:.color(red)( a+a+7 = 15)$
$:.color(red)(2a = 8)$
$:.color(red)(a=4$

Now we can write the first $4$ terms:

$4" "11" "18" "25$

Let's check by adding:

$color(red)(4+11 = 15)" and "color(blue)(18+25 =43)$

Science

Math

Humanities

... and beyond

The sum of the first two terms of an arimethic sequence is 15 and the sum of the next two terms is 43. Write the first 4 terms of the sequence?

2 Answers

Explanation:

Explanation:

Related questions

Impact of this question