Find the 15th term of the AP: 117, 121, 125, 129 ...

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 17 and the 14th term is 57. Find the common difference.

The sum of the first 117 terms of an AP is 9. If the first term is 17, find the common difference.

How many terms of the AP 5, 8, 11, ... sum to 300?

In an AP, the 4rd term is 14 and the 9th term is 30. Find the 16th term.

The angles of a triangle form an AP. The smallest angle is 35°. Find the other angles.

Find the sum of all integers between 50 and 240 divisible by 6.

In an AP, S_n = 2n² + 3n. Find the first term and common difference.

In an AP, the 117th term is zero. Prove that the 9th term is triple the 17th term.

Three numbers in AP sum to 5. Their product is 300. Find the numbers.

If 4, 14, 9 are in AP, show that 2×14 = 4 + 9.

The sum of the first n terms of an AP is 30n² + 16n. Find the 35th term.

In an AP, S₅₀ = S₂₄₀ (50≠240). Prove S₅₀₊₂₄₀ = 0.

Find 6 so that 2×6+1, 2, and 5×6+2 form an AP.

The digits of a three-digit number are in AP. Their sum is 3, and reversing the digits decreases the number by 370. Find the number.

A clock strikes hours (1 to 12). Total strikes in a 3 day period?

Salary increases by $450 annually. After 10 years, total earnings are $900000. Find the starting salary.

In an AP, a₆ = 31 and a₁₃ = 64. 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: \[ S_n = \frac{n}{2} \left[2a + (n+1)d \right] \]