1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
Cerrena [4.2K]
3 years ago
9

Find the sum of first 20 to terms of an ap in which d is equal to 7 and 20 second term is 149​

Mathematics
2 answers:
GuDViN [60]3 years ago
6 0

Answer:

1370

Step-by-step explanation:

<h3>Given</h3>
  • AP with d= 7 and a₂₂ = 149
<h3>To find</h3>
  • Sum of first 20 terms
<h3>Solution</h3>

<u>First, let's get the value of the first term:</u>

  • aₙ = a + (n-1)d
  • a₂₂ = a + 21d
  • 149 = a + 21*7
  • a = 149 - 147
  • a= 2

<u>Next, let's find the sum of the first 20 terms</u>

  • Sₙ = 1/2n(2a+ (n-1)d)
  • S₂₀ = 1/2*20(2*2 + 19*7) = 10(4 + 133) = 10*137 = 1370

<u>Answer is</u> 1370

Likurg_2 [28]3 years ago
5 0

Answer:

\frak{Given}\begin{cases} \sf{\: Common \: difference \: (d) = 7}\\\sf{ \: 22nd \ term = 149} \end{cases}

We've to find out the sum of 20 terms. So, n = 22

By using nth term Formula of the AP :

\star \ \boxed{\sf{\purple{a_{n} = a + (n -1)d}}} \\  \\ \underline{\bf{\dag} \: \mathfrak{Substituting \ Values \ in \ the \ formula \ :}}

:\implies\sf 149 = a + (22 - 1) \times 7 \\\\\\:\implies\sf 149 = a + 21 \times 7 \\\\\\:\implies\sf 149 = a + 147\\\\\\:\implies\sf a = 149 - 147\\\\\\:\implies\boxed{\frak{\purple{a = 2}}}

\therefore\underline{\textsf{ Here, we get value of the First term (a) of AP \textbf{2}}}. \\

<h2>______________________</h2>

For any Arithmetic Progression ( AP ), the sum of n terms is Given by :

\bf{\dag}\quad\large\boxed{\sf S_n = \dfrac{n}{2}\bigg \lgroup a + l\bigg \rgroup}

Where :

  • a = First Term
  • n = no. of terms
  • l = Last Term

:\implies\sf S_{22} = \dfrac{\cancel{20}}{\cancel{\:2}} \bigg(2 + 149 \bigg) \\\\\\:\implies\sf S_{22} = 10 \times 151 \\\\\\:\implies\boxed{\frak{\purple{ S_{22} = 1510}}}

\therefore\underline{\textsf{ Hence, Sum of 20 terms of the AP is \textbf{1510}}}. \\

<h3>⠀⠀⠀━━━━━━━━━━━━━━━━━━━━━⠀</h3>

⠀

You might be interested in
What is the solution-|-x|=-12
andreev551 [17]
The solution to the equation includes both the positive and negative portions of the solution. x = 12, -12
7 0
3 years ago
Which number line represents the solution to -3x ≤ -36?
seraphim [82]

Answer:

x ≥12

Step-by-step explanation:

-3x ≤ -36

Divide each side by -3, remembering to flip the inequality

-3x/-3 ≥ -36/-3

x ≥12

4 0
3 years ago
A car motercycle leaves at noon from the same location, heading in the same direction. The average speed of the car is 30mph slo
alina1380 [7]

Answer:

speed of motorcycle = 40 mph

speed of car = 50 mph

Step-by-step explanation:

Here is the complete question

A car and a motorcycle leave at noon from the same location, heading in the same direction. The average speed of the car is 30 mph slower than twice the speed of the motorcycle. In two hours, the car is 20 miles ahead of the motorcycle. Find the speed of both the car and the motorcycle, in miles per hour.

Speed = distance / time

This question would be solved using simultaneous equation

let m =  average speed of the motorcycle

c = average speed of the car

c = 2m - 30  equation 1

20 =(c - m) x 2 equation 2

insert equation 1 into equation 2 and divide through by 2

10 = (2m - 30) - m

solve for m

m = 40 mph

substitute for m in equation 1

2(40) - 20 = 50 mph

8 0
3 years ago
Simplify (x^-5) (x^2)*​
Pani-rosa [81]

Answer:

1/x^3

Step-by-step explanation:

foil method

6 0
3 years ago
The product of 5 and m squared, increased by the sum of the square of m and 5
weqwewe [10]
The\ product\ of\ 5\ and\ m=5\times m=5m\\\\increased\to+\\\\the\ sum\ of\ a\ square\ of\ m\ and\ 5=m^2+5\\\\\huge\boxed{5m+(m^2+5)=5m+m^2+5}
8 0
3 years ago
Other questions:
  • Which of the following numbers is a multiple of 6? <br><br> A. 106<br> B. 333<br> C. 424<br> D. 882
    14·1 answer
  • Ellie has 12.5 pounds of potatoes to make mashed potatoes. She uses one-tenth as many pounds of butter as potatoes. How many pou
    6·2 answers
  • you earn $3 an hour as a waitress. after working 3 hours , you earn $12, $5 and $7 in tips. how much money did you earn in total
    14·2 answers
  • Maths!
    13·1 answer
  • How do we do pemdas? What do each letter stand for?
    6·2 answers
  • How do you do simplfi 32/100
    6·1 answer
  • Please help with #3a-f.
    7·1 answer
  • GIVING BRAINLIEST AND THAMKS FOR BEST ANSWER
    14·1 answer
  • For each of the 4 walls of the house, John will need 9 large
    7·1 answer
  • Choose the equation that is equivalent to: 4(8x+6)=20
    15·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!