In an APTN minusTN -1 is equal to
Answers
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.