Series — AS & A Level Mathematics (9709) questions by topic

The third term of a geometric progression is 18 and the sum of the first three terms is 26. It is given that the common ratio is negative. Find the tenth term of the progression.…

Find the first three terms, in ascending powers of x, in the expansion of each of the following expressions. (2 − px)^5

The coefficient of x^7 in the expansion of (px^2 + (4/p) x)^5 is 1280. Find the value of the constant p.

The first, second and third terms of an arithmetic progression are 4k, k^2 and 8k respectively, where k is a non-zero constant. Find the value of k.

The first two terms of a geometric progression are 4 sin²θ, 8 sin³θ, where θ is an angle such that 0 < θ < (1/6)π. Given that the sum to infinity of the progression is 1/2, find…

Find the first three terms in the expansion of (2 − (3/2)x)^5 in ascending powers of x.

An arithmetic progression has first term a and common difference 2. The Nth term is 55 and the sum of the first 3N terms is 5760. Find the values of N and a.

In the expansion of (3 + ax)^5 + (6 − x)^4, the coefficient of x^2 is six times the coefficient of x. Find the possible values of the constant a. [5]

Each year, on her birthday, Ananya receives some money from each of her parents. On Ananya's first birthday, her father gives her $10. Every subsequent year, her father gives her…

Expand (6 - x)(1 - 2x)^(-3/2) in ascending powers of x, up to and including the term in x^2, simplifying the coefficients. [4]

The coefficient of x² in the expansion of (1 − 4x)⁶ is 12 times the coefficient of x² in the expansion of (2 + ax)⁵. Find the value of the positive constant a.

The first and second terms of an arithmetic progression are tan θ and sin θ respectively, where 0 < θ < ½π. Given that θ = ¼π, find the exact sum of the first 40 terms of the…

Find the coefficient of x^2 in the expansion of (2 − 5x)(1 + 3x)^10.

The first term of an arithmetic progression is 1.5 and the sum of the first ten terms is 127.5. Find the common difference.

The geometric progression a₁, a₂, a₃, … has first term 2 and common ratio r where r 0. It is given that (9/2)a₅ + 7a₃ = 8. Find the value of r.

Expand (3 + x)(1 − 2x)^(1/2) in ascending powers of x, up to and including the term in x², simplifying the coefficients.

In the expansion of (kx + 2/x)⁴, where k is a positive constant, the term independent of x is equal to 150. Find the value of k and hence determine the coefficient of x² in the…

An arithmetic progression has first term 5 and common difference d, where d 0. The second, fifth and eleventh terms of the arithmetic progression, in that order, are the first…

The first term of an arithmetic progression is −20 and the common difference is 5. Find the sum of the first 20 terms of the progression.

Find the term independent of x in the expansion of the following: (x + 3/x²)⁶.

An arithmetic progression has fourth term 15 and eighth term 25. Find the 30th term of the progression.

Find the coefficients of x³ and x⁴ in the expansion of (3 − ax)⁵, where a is a constant. Give your answers in terms of a.

The first term of a convergent geometric progression is 10. The sum of the first 4 terms of the progression is p and the sum of the first 8 terms of the progression is q. It is…

Expand (9 − 3x)^(1/2) in ascending powers of x, up to and including the term in x², simplifying the coefficients.

Find the first three terms in the expansion, in ascending powers of x, of (2 + 3x)⁴.

The first three terms of an arithmetic progression are p²/6, 2p − 6 and p. Given that the common difference of the progression is not zero, find the value of p.

The coefficient of x⁴ in the expansion of (x + a)⁶ is p and the coefficient of x² in the expansion of (ax + 3)⁴ is q. It is given that p + q = 276. Find the possible values of the…

The second term of a geometric progression is 16 and the sum to infinity is 100. Find the two possible values of the first term.

Give the complete expansion of (x + 2/x)⁵.

A progression has first term a and second term a²/(a + 2), where a is a positive constant. For the case where the progression is geometric and the sum to infinity is 264, find the…

Find the coefficient of x³ in the binomial expansion of (3 + x)√(1 + 4x).

Expand (1 + 3x)⁶ in ascending powers of x up to, and including, the term in x².

The sum of the first two terms of a geometric progression is 15 and the sum to infinity is 125/7. The common ratio of the progression is negative. Find the third term of the…

The coefficient of x³ in the expansion of (3 + 2ax)⁵ is six times the coefficient of x² in the expansion of (2 + ax)⁶. Find the value of the constant a.

The first, second and third terms of a geometric progression are sin θ, cos θ and 2 − sin θ respectively, where θ radians is an acute angle. Find the value of θ.

Expand the following in ascending powers of x up to and including the term in x². (1 + 2x)⁵

The first, second and third terms of a geometric progression are 2p + 6, 5p and 8p + 2 respectively. Find the possible values of the constant p.