Find the 15th term of the AP: 305, 309, 313, 317 ...

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

In an AP, the 6th term is 21 and the 14th term is 69. Find the common difference.

The sum of the first 305 terms of an AP is 10. If the first term is 21, find the common difference.

How many terms of the AP 6, 9, 12, ... sum to 330?

In an AP, the 3rd term is 15 and the 8th term is 35. Find the 20th term.

The angles of a triangle form an AP. The smallest angle is 30°. Find the other angles.

Find the sum of all integers between 60 and 160 divisible by 6.

In an AP, S_n = 5n² + 5n. Find the first term and common difference.

In an AP, the 305th term is zero. Prove that the 10th term is triple the 21th term.

Three numbers in AP sum to 6. Their product is 330. Find the numbers.

If 3, 15, 8 are in AP, show that 2×15 = 3 + 8.

The sum of the first n terms of an AP is 35n² + 20n. Find the 30th term.

In an AP, S₆₀ = S₁₆₀ (60≠160). Prove S₆₀₊₁₆₀ = 0.

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

The digits of a three-digit number are in AP. Their sum is 5, and reversing the digits decreases the number by 360. Find the number.

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

Salary increases by $500 annually. After 8 years, total earnings are $900000. Find the starting salary.

In an AP, a₄ = 28 and a₁₅ = 62. Find a₁₈.

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