Find the 15th term of the AP: 109, 113, 117, 121 ...

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 19 and the 14th term is 67. Find the common difference.

The sum of the first 109 terms of an AP is 9. If the first term is 19, find the common difference.

How many terms of the AP 6, 9, 12, ... sum to 290?

In an AP, the 4rd term is 12 and the 10th term is 25. Find the 18th 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 100 and 230 divisible by 6.

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

In an AP, the 109th term is zero. Prove that the 9th term is triple the 19th term.

Three numbers in AP sum to 6. Their product is 290. Find the numbers.

If 4, 12, 10 are in AP, show that 2×12 = 4 + 10.

The sum of the first n terms of an AP is 25n² + 18n. Find the 35th term.

In an AP, S₁₀₀ = S₂₃₀ (100≠230). Prove S_100+230 = 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 2, and reversing the digits decreases the number by 330. Find the number.

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

Salary increases by $400 annually. After 11 years, total earnings are $800000. Find the starting salary.

In an AP, a₅ = 34 and a₁₃ = 66. Find a₂₂.

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: \[ S_n = \frac{n}{2} \left[2a + (n+1)d \right] \]