Which number will lie in place of $\star$ in the sequence: 8, 14, 26, 50, $\star$ ?
98
Differences between consecutive terms: 14-8=6, 26-14=12, 50-26=24. Each difference doubles the previous one (6, 12, 24, 48...). So the next difference is 48, giving the next term = 50 + 48 = 98. Hence option (B) is correct.
Important Questions from Sequences and Series
The fifth term of an AP of n terms, whose sum is n 2– 2n, is
A person is to count 4500 notes. Let a ndenote the number of notes he counts in the nth minute. If a 1= a 2= a 3= … = a 10 = 150, and a 10 , a 11 , a 12 , … are in AP with the common difference -2, then the time taken by him to count all the notes is
- \(\mathop {\lim }\limits_{n \to \infty } {\left( {1 - \frac{1}{{2n}}} \right)^{n + 1}}\) is equal to
If \({S_n} = nP + \frac{{n\left( {n - 1} \right)Q}}{2}\) , where S ndenotes the sum of the first n terms of an AP, then the common difference is
What is the sum of the first 12 terms of an arithmetic progression if the 3rd term is -13 and the 6th term is -4?
