Concepts discussed on May 19, 2018
Arithmetic  Progressions
Welcome to the live session of Progressions. The concepts and questions discussed on May 19, 2018 during the live session follow the embedded video. The video link next to each concept will take you to the start of the part of the video where that specific concept is discussed. Click the video embedded below to watch the entire session.

If 4 times the 4th term of an A.P. is equal to 9 times the 9th term of the A.P., what is 13 times the 13th term of this A.P.?

The sum of three terms in A.P. is –6 and the product is 2^{6}, find the common difference of this sequence.

The sum up to n terms of an A.P. is 2n^{2} + n, what is the 12th term of this A.P.?

If S_{n} = n^{3} – 2n^{2} + 4n + 3 and t_{k} = 27, find k.

The product of the first 5 terms of a G.P. is 32. The sum of the first and third terms is 5. Find the 7th term of this G.P.

The sum of first three terms of a GP is 19, the sum of the next three terms is 57. What is the sum of the first 12 terms of this G.P.?

The sum of three terms in a G.P. is 14, and the sum of their squares is 84. Which of the following is a possible value of the product of the first 4 terms of this G.P.?
 128
 512
 96
 64

An infinite G.P. has as its first term a and sum = 8. What is the range of values ‘a’ can take?

Consider a sequence of positive integers where (a_{n})^{2} = a_{n1} × a_{n+1}. The sum of the 4^{th}, 5^{th} and 6^{th} terms is 112 and the product of the 1^{st} three terms is 64. Find the sum up to 5 terms of this sequence.

A, B, C are three terms in G.P. that add up to 39. A, B + 6 and C are in AP. If A × B2 > C, find the product of A and C.

a, b, c and d are in A.P., What can we say about terms bcd, acd, abd and abc?
 They are also in A.P.
 They are in H.P.
 They are in G.P.
 They are not in an A.P.,G.P., or H.P.