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Arithmetic Progressions
EXAMPLES
CBSE_NCERT_TEXTBOOK
Grade 10
Question:
Find the 11th term from the last term (towards the first term) of the AP : 10, 7, 4, . . ., – 62.
Step-by-Step Solution
Key Concept: Use the nth term formula of an AP, $a_n = a + (n-1)d$, to determine the total number of terms. Then locate the required term by counting backwards from the last term.
1. Identify the first term and common difference: $$a = 10, \quad d = 7-10 = -3.$$\ 2. Let the total number of terms be $n$. The last term $a_n$ is given as $-62$. $$a_n = a + (n-1)d = -62.$$\ 3. Substitute $a$ and $d$: $$10 + (n-1)(-3) = -62$$ $$-3(n-1) = -72$$ $$n-1 = 24 \Rightarrow n = 25.$$\ 4. The 11th term from the last term means we move 10 positions towards the first term. Hence the required term is the $(n-10)^{\text{th}}$ term: $$\text{Required term} = a_{n-10} = a_{25-10}=a_{15}.$$\ 5. Compute the 15th term using the nth term formula: $$a_{15} = a + (15-1)d = 10 + 14(-3) = 10 - 42 = -32.$$\ 6. Therefore, the 11th term from the last term is $-32$.
Correct Answer:-32
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