Math, asked by pbqgrecha1, 16 days ago

In an APTN minusTN -1 is equal to

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Answered by linanguyenyt
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Answer:

1) b

2) d

3) a

4) a

5) c

6) c

7) c

8) b

Step-by-step explanation:

The sum of n terms is also equal to the formula where l is the last term

Tn = Sn - Sn-1 , where Tn = nth term.

When three quantities are in AP, the middle one is called as the arithmetic mean of the other two.

If a, b and c are three terms in AP then b = (a+c)/2.

The general form of an Arithmetic Progression is a, a + d, a + 2d, a + 3d and so on. Thus nth term of an AP series is Tn = a + (n - 1) d, where Tn = nth term and a = first term. Here d = common difference = Tn - Tn-1.

3)if they are in ap their common difference will be same.

so,

(b+3) - (b-1) = (3b-1) - (b+3)

b+3-b+1 = 3b - 1 -b -3

4 = 2b - 4

2b = 8

b = 4.

4)

a+2d=12

a+6d=24

Solving the equations, we get

a=6,d=3

t₁₀ =5+(9×3)=33

5)

Let us assume the second number is a and the difference between consecutive numbers is d.

According to Arithmetic progression,

First number = a - d

Second number = a

Third number = a + d

According to question,

Sum of the all three numbers = 15

a - d + a + a + d = 15

3a = 15

a = 5

Again according to given question,

sum of square of the 3 numbers = 83

(a - d) 2 + a 2 + (a + d) 2 = 83

apply the algebra formula

a 2 + d 2 - 2ad + a 2 + a 2 + d 2 + 2ad = 83

3a 2 + 2d 2 = 83

Put the value of a in above equation.

3 x 5 2 + 2d2 = 83

3 x 25 + 2d2 = 83

75 + 2d2 = 83

2d 2 = 83 - 75

2d 2 = 8

d 2 = 8/2

d 2 = 4

d = 2

Put the value of a and d in below equation.

First number = a - d = 5 - 2 = 3

Second number = a = 5

Third number = a + d = 5 + 2 = 7

The smallest number is 3.

7)

Given 5 times 5th  term 8 times 8th  term

5(a+(5−1)d)=8(a+(8−1)d) ---- [ tn =a+(n−1)d ]

5a+20d=8a+56d

⇒3a+36d=0

∴a+12d=0

Comparing this with a+(n−1)d,

we get ,n−1=12

n=13th  term.

Hence, 13th  term is zero.

8)

The third term is 6.

Explanation:

Let the 5 numbers in AP be a-2d, 2-d, a, a+d, a+2d

Given that, the sum of 5 numbers in AP is 30.

Therefore, (a-2d)+ (a-d)+a+(a+d)+(a+2d) = 30

5a = 30

a=30/5 = 6

Hence, the third term of an AP is 6.

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