Question

Serena, Dawn, May, Misty, Angie, Miette, Melody, Bianca(Movie One Not The Black And White One) All Love Ash?

Answer 1

Answer:

Use Euclid’s division algorithm to find the H.C.F. of

(i) 184, 230 and 276

(ii) 136,170 and 255

Answer 2

Serena, Dawn, May, Misty, Angie, Miette, Melody, Bianca(Movie One Not The Black And White One) All Love Ash?Serena, Dawn, May, Misty, Angie, Miette, Melody, Bianca(Movie One Not The Black And White One) All Love Ash?Serena, Dawn, May, Misty, Angie, Miette, Melody, Bianca(Movie One Not The Black And White One) All Love Ash?Serena, Dawn, May, Misty, Angie, Miette, Melody, Bianca(Movie One Not The Black And White One) All Love Ash?Answer:

First term of the progression is 1.

Last term of the progression is 109.

Step-by-step explanation:

Given that:

An arithmetic progression consists of 37 terms.

The sum of the first 3 terms of is 12.

The sum of the last 3 terms is 318.

To Find:

The first and last terms of the progression.

Formula used:

aₙ = a + (n - 1)d

Where,

aₙ = nth terms

a = First term

d = Common difference

Let us assume:

First term be a.

Common difference be d.

Last term be l.

Sum of the first 3 terms:

⟿ a + a + d + a + 2d = 12

⟿ 3(a + d) = 12

⟿ a + d = 12/3

⟿ a + d = 4

⟿ a = 4 - d ______(i)

Sum of the last 3 terms:

⟿ l + l - d + l - 2d = 318

⟿ 3(l - d) = 318

⟿ l - d = 318/3

⟿ l - d = 106

Last term is 37.

⟿ a₃₇ - d = 106

⟿ a + 36d - d = 106

⟿ a + 35d = 106

Substituting the value of a from eqⁿ(i).

⟿ 4 - d + 35d = 106

⟿ 34d = 106 - 4

⟿ 34d = 102

⟿ d = 102/34

⟿ d = 3 ______(ii)

Finding the first term:

Now in equation (i).

⟿ a = 4 - d

Substituting the value of d from eqⁿ(ii).

⟿ a = 4 - 3

⟿ a = 1

∴ First term = 1

Finding the last term:

⟿ l = a₃₇

⟿ l = a + (37 - 1)d

Substituting the value of a and d.

⟿ l = 1 + (36 × 3)

⟿ l = 1 + 108

⟿ l = 109

∴ Last term = 109