If the first term of an A.P. is 3 and the sum of its first...

If the first term of an A.P. is 3 and the sum of its first 25 terms is equal to the sum of its next 15 terms, then the common difference of this A.P. is :
(a) $\frac{1}{6}$
(b) $\frac{1}{5}$
(c) $\frac{1}{4}$
(d) $\frac{1}{7}$

Labs

Want to see this concept in action?

NEW

Explore this concept interactively to see how it behaves as you change inputs.

View Labs

Key Concepts

Arithmetic Progression

An arithmetic progression (AP) is a sequence of numbers in which the difference between consecutive terms is constant, known as the common difference. Its general term is expressed as a? = a + (n-1)d, where a represents the first term and d is the constant difference between the terms.

Sum Formula of an Arithmetic Progression

The sum of the first n terms of an arithmetic progression is given by the formula S? = n/2 × [2a + (n-1)d]. This formula is fundamental in solving problems related to the accumulated total of a series of terms in an AP, facilitating the bridge between term relationships and cumulative totals.

Equating Partial Sums

When a problem involves setting the sum of one segment of an arithmetic progression equal to the sum of another segment, this condition creates an equation that can be solved for unknown variables, such as the common difference. This involves writing separate sum expressions for the designated segments using the sum formula and then equating them to establish a relationship.

Transcript

Please give Ace some feedback