How many terms are there in an A.P. whose first and fifth terms are $-14$ and $2$, respectively and the last term is $62$ ?
Generated by claude-sonnet-4-6 · 2026-06-15 10:31 · grounding rag
Model Answer
Given: $a = -14$, $a_5 = 2$, $l = a_n = 62$
Step 1: Find common difference $d$
Using $a_5 = a + 4d$:
$$2 = -14 + 4d \implies 4d = 16 \implies d = 4$$
Step 2: Find number of terms $n$
Using $a_n = a + (n-1)d$:
$$62 = -14 + (n-1) \times 4$$
$$76 = (n-1) \times 4$$
$$n - 1 = 19$$
$$n = 20$$
∴ There are 20 terms in the AP.
Source: Chapter 5, Section 5.2 (nth term formula)
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Explanation
- First find $d$ using the 5th term condition — this is the key intermediate step examiners look for (1 mark).
- Then apply $a_n = a + (n-1)d$ with the last term to find $n$ (1 mark each for correct substitution and answer).
- Always state the formula before substituting — it earns a method mark even if arithmetic slips.