Find the 15th term of the AP: 273, 277, 281, 285 ...

The first term of an AP is 9, and the common difference is -3. Find the 10th term.

In an AP, the 6th term is 22 and the 14th term is 54. Find the common difference.

The sum of the first 273 terms of an AP is 9. If the first term is 22, find the common difference.

How many terms of the AP 4, 7, 10, ... sum to 320?

In an AP, the 3rd term is 15 and the 10th term is 30. Find the 21th term.

The angles of a triangle form an AP. The smallest angle is 40°. Find the other angles.

Find the sum of all integers between 100 and 210 divisible by 7.

In an AP, S_n = 2n² + 4n. Find the first term and common difference.

In an AP, the 273th term is zero. Prove that the 9th term is triple the 22th term.

Three numbers in AP sum to 4. Their product is 320. Find the numbers.

If 3, 15, 10 are in AP, show that 2×15 = 3 + 10.

The sum of the first n terms of an AP is 30n² + 21n. Find the 40th term.

In an AP, S₁₀₀ = S₂₁₀ (100≠210). Prove S_100+210 = 0.

Find 7 so that 2×7+1, 2, and 5×7+2 form an AP.

The digits of a three-digit number are in AP. Their sum is 4, and reversing the digits decreases the number by 310. Find the number.

A clock strikes hours (1 to 12). Total strikes in a 2 day period?

Salary increases by $450 annually. After 9 years, total earnings are $870000. Find the starting salary.

In an AP, a₆ = 29 and a₁₅ = 67. Find a₂₀.

Prove that the sum of the first \( n \) terms of an arithmetic progression (AP) is given by: \[ \frac{n}{2} \left[ 2a + (n - 1)d \right] \]

Given an arithmetic progression (AP) with first term 𝑎 = 5 and common difference 𝑑 = 3, complete the table below using:

• The \(n-th\) term formula: \[ T_n = a + (n-1)d \]
• The sum of the first \(n\) term formula: \[ S_n = \frac{n}{2} \left[2a + (n+1)d \right] \]