IAT (IISER) 2025 | Sequences and Series Question 1 | Mathematics

Let $S_n$ denote the sum of the first $n$ terms of a sequence $a_1, a_2, a_3, \ldots$. If $S_{n+3}-S_n=13 n+7$ for all $n$, what is the value of $a_{13}-a_{10}$ ?

137

IAT (IISER) 2024

MCQ (Single Correct Answer)

-1

Let $a_1, a_2, a_3, \ldots$ be a sequence of real numbers. Let $s_n=a_1+a_2+\cdots+a_n$. If $2 s_n=$ $n\left(c+a_n\right)$ for some real number. for some real number $c$ and for all $n=1,2,3, \ldots$, then which one of the following statements is Correct?

$a_1, 2 a_2, 3 a_3, \ldots$ is an Arithmetic Progression.

$a_1, a_2, a_3, \ldots$ is an Arithmetic Progression.

$a_1, 2 a_2, 3 a_3, \ldots$ is a Geometric Progression.

$a_1, a_2, a_3$, ...is a Geometric Progression.

IAT (IISER) 2022

MCQ (Single Correct Answer)

-1

A lab reports that the global average temperature in the year 2020 was $14.9^{\circ} \mathrm{C}$ and predicts that the global average temperature will increase at the rate of $1 \%$ per year. What will be the global average temperature in the year 2035?

$15.049^{\circ} \mathrm{C}$

$17.298^{\circ} \mathrm{C}$

$17.135^{\circ} \mathrm{C}$

$17.471^{\circ} \mathrm{C}$

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