If 9th term of an AP is zero, prove that its 29th term is double of its 19th term.

3

(a)

Find the value of the middle term of the following AP: -6, -2, 2, ....., 58

3

(a)

Determine the AP whose fourth term is 18 and the difference of the ninth term from the fifteenth term is 30.

3

(a)

How many numbers lie between 10 and 300, which when divided by 4 leave a remainder 3?

3

(a)

The 2nd, 31st and the last term of an AP are 7\(\frac{3}{4}\), \(\frac{1}{2}\) and -6\(\frac{1}{2}\), respectively. Find the first term and number of terms. 

3

(a)

Find the sum: \(\frac{a - b}{a + b}+\frac{3a - 2b}{a + b}+\frac{5a - 3b}{a + b}+...\) to 11 terms.

3

(a)

a₁, a₂, a₃,......,a₂₄ are in AP and a₁ + a₅ + a₁₀ + a₁₅ + a₂₀ + a₂₄ = 300. Find the sum of first 24 terms of the AP.

3

(a)

If S_n denotes the sum of n terms of an AP whose common difference is d, show that d = S_n - 2S_n-1 + S_n-2.

3

(a)

If T₁, T₂, T₃,......, T_n are consecutive terms of an AP, then prove that \(\frac{1}{T_1T_2}+\frac{1}{T_2T_3}+.....+\frac{1}{T_{n-1}T_n}+\frac{n-1}{T_1.T_n}\)

3

(a)

In the following A.P., find the missing term: 9, ...., ...., ....., 25

3

(a)

If sum of three numbers in A.P. is 21 and their product is 231. Find the numbers.

3

(a)

Find three numbers in A.P. whose sum is 15 and the product is 80.

3

(a)

The sum of first three terms of an A.P. is 33. If the product of the first and third term exceeds the second term by 29, find the A.P.

3

(a)

If the sum of the first 14 terms of an AP is 1050 and its first term is 10, find the 20th term.

3

(a)

The sum of the third and the seventh terms of an AP is 6 and their product is 8. Find the sum of first sixteen terms of the AP.

3

(a)