Sequences & Series
Sequences And Series
nta_abhyas_2025
Grade 11
Question:
If $a, b, c, d, e, f$ are in arithmetic progression. Then $e - c$ is equal to
2(c - a)
2(f - d)
2(d - c)
d - c
Step-by-Step Solution
Key Concept: The sum of an AP is $S_n = \frac{n}{2}(a_1 + a_n)$, which directly uses the first and last terms.
Given $2(a_1 + a_{19}) = 224$, we find $a_1 + a_{19} = 112$. Using the formula for the sum of an arithmetic progression, $S = \frac{n}{2}(a_1 + a_n)$, we have $S = \frac{19}{2} \times 112 = 19 \times 56 = 1064$. This uses the property that in an AP, the sum depends only on the first term, last term, and number of terms.
Correct Answer: 1064