Important Questions: Arithmetic Progressions - Class 10 MCQ

The first term of the given arithmetic progression (AP) is:

a = 4/3

To find the common difference d, we can subtract the first term from the second term:

d = (1/3) - (4/3) = (1 - 4)/3 = -3/3 = -1

So, the first term and common difference are respectively:

Answer: (b) 4/3, -1

∵ p, q, r are in AP.
∴ 2 q = p + r
⇒ p + r - 2 q = 0

Let next term be T4

The given AP is √8, √18, √32,......... On simplifying the terms, we get: 

a₁₀₁ = 3.5 + 0 (100) = 3.5

Johann Friedrich Gauss, he was a German mathematician who find the sum of the first 100 natural number.

-10+4 = -6
-6 + 4 = -2
-2 + 4 = 2
so clearly d = 4

The given AP is 5, 2, -1, -4 ... ...., -31
d = 2 - 5 = -3, so d for the AP starting from the last term is 3.
The first term = l = -31
We know, a_n = a+(n−1)d
a₆ from the end = −31+(5)3
a₆ from the end = −16

a₄ - b₄ = (a₁ + 3d) - (b₁ + 3d)
= a₁ b₁ = - 1 - (-8) = 7

Let nth term of the given AP be 210.
Here, first term,
a = 21
And common difference,
d = 42 – 21 = 21 and
an = 210

⇒ 210 = 21 + (n - 1)21
⇒ 210 = 21 + 21n - 21
⇒ 210 = 21n
⇒ n = 10
Hence, the 10th term of the AP is 210.