Sequences & Series
Two APs — Common Difference Relation, Finding a₁
nta_pyq_2026_jan
Grade 11
Question:
The common difference of the A.P. $a_1,a_2,\ldots,a_m$ is 13 more than the common difference of the A.P. $b_1,b_2,\ldots,b_n$. If $b_{31}=-277$, $b_{43}=-385$ and $a_{78}=327$, then $a_1$ is equal to
Step-by-Step Solution
Key Concept: From $\{b_n\}$: $b_{43}-b_{31}=12d_b=-108\Rightarrow d_b=-9$. $d_a=d_b+13=4$. $a_{78}=a_1+77d_a=327$.
$a_1=19$.
Correct Answer: 3