Mathematics, 03.08.2020 14:01 chandranewlon

The sum of the first 16th term of an A. P is 240 and the sum of the next 4 term is 220 find the next term of the A. P

Answers: 3

Show answers

Answers

Answer from: aashna66

Step-by-step explanation:

The sum of the first 16 terms of an arithmetic progression (A.P) is 240

The sum of the next 4 terms is 220

The sum of n terms in an A.P is given by;

$s_{n}$ = n/2(2a + (n - 1)d)

240 = 8(2a + 15d) ... (i)

460 = 10(2a + 19d) .... (ii)

Simplifying this gives;

2a + 15d = 30 ... (i)

2a + 19d = 46 ... (ii)

Subtracting (i) from (ii) we get;

4d = 16

d (common difference) = 4

and a (first term) = (30 - 60)/ 2 = -15

The sequence upto 21 terms is here:

-15, -11, -7, -3, 1, 5, 9, 13, 17, 21, 25, 29, 33, 37, 41, 45, 49, 51, 55, 59, 61, 65

So the next term (21^st term) is 65.

Answer from: coopera1744

a₂₁ = 65

Step-by-step explanation:

The Sum of an Arithmetic Progression is the sum of the first term plus the sum of the last term divided by 2 and multiplied by the number of terms.

$a_1\ \text{is the first term}\\a_n=a_1+d(n-1)\quad \text{is the value of the nth term}\\\\$

Let's find the 16th term (n = 16)

$a_{16}=a_1+d(16-1)\\\\.\quad =a_1+15d$

Now let's find the sum of the first 16 terms. This will be Equation 1:

$S_{16}=\dfrac{(a_1)+(a_1+15d)}{2}\times 16=240\\\\\\.\qquad 8(2a_1+15d)=240\\\\\\.\qquad 2a_1+15d=30\qquad \leftarrow \text{Equation 1}$

************************************************************************************

Repeat what we did above for the next 4 terms (n = 17 to n = 20). This will be Equation 2:

$a_{17}=a_1+d(17-1)\\\\.\quad =a_1+16d\\\\\\a_{20}=a_1+d(20-1)\\\\.\quad =a_1+19d$

$S_{17-20}=\dfrac{(a_1+16d)+(a_1+19d)}{2}\times 4=220\\\\\\.\qquad 2(2a_1+35d)=220\\\\\\.\qquad 2a_1+35d=110\qquad \leftarrow \text{Equation 2}$

*********************************************************************************************

Now we have a system of equations. Solve using the Elimination Method:

2a₁ + 15d = 30 → -1(2a₁ + 15d = 30) → -2a₁ - 15d = -30

2a₁ + 35d = 110 → 1(2a₁ + 35d = 110) → 2a₁ + 35d = 110

20d = 80

d = 4

Input d = 4 into one the equations to solve for a₁:

Equation 1: 2a₁ + 15d = 30

2a₁ + 15(4) = 30

2a₁ + 60 = 30

2a₁ = -30

a₁ = -15

Given a₁ = -15 and d = 4, we can find the next term (n = 21)

$a_n=a_1+d(n-1)\\\\a_{21}=-15+4(21-1)\\\\.\quad =-15+4(20)\\\\.\quad = -15+80\\\\.\quad = 65$

Answer from: Quest

the answer would be c: ax + b = ax + c

step-by-step explanation:

Answer from: Quest

step-by-step explanation:

Another question on Mathematics

Mathematics, 21.06.2019 20:00

Which type of graph would allow us to compare the median number of teeth for mammals and reptiles easily

Answers: 2

Answer

Mathematics, 21.06.2019 20:10

Suppose g(x) = f(x + 3) + 4. which statement best compares the graph of g(x) with the graph of f(x)?

Answers: 2

Answer

Mathematics, 21.06.2019 23:30

If the car had not hit the fence, how much farther would it have skidded? solve the skid-distance formula to find the extra distance that the car would have traveled if it had not hit the fence. round your answer to two decimal places. note that unit conversion is built into the skid distance formula, so no unit conversions are needed.

Answers: 2

Answer

Mathematics, 21.06.2019 23:30

The average daily maximum temperature for laura’s hometown can be modeled by the function f(x)=4.5sin(πx/6)+11.8 , where f(x) is the temperature in °c and x is the month. x = 0 corresponds to january.what is the average daily maximum temperature in may? round to the nearest tenth of a degree if needed.use 3.14 for π .

Answers: 1

Answer

You know the right answer?

The sum of the first 16th term of an A. P is 240 and the sum of the next 4 term is 220 find the next...

Questions