Sequences & Series
AP Written in Rows — Sum of 10th Row
nta_pyq_2024_apr
Grade 11
Question:
An arithmetic progression is written in the following way: Row 1: 2; Row 2: 5,8; Row 3: 11,14,17; Row 4: 20,23,26,29; $\ldots$ The sum of all the terms of the 10th row is
Step-by-Step Solution
Key Concept: The AP is $2,5,8,11,\ldots$ with $d=3$. The $k$th row has $k$ terms. Row 10 starts at the $(1+2+\cdots+9+1)=46$th term. First term of row 10: $a_{46}=2+45\times3=137$. Last term: $a_{55}=2+54\times3=164$.
Row 10: first term $137$, last $164$. Sum $=5\times(137+164)=1505$.
Correct Answer: 1505