Sequences & Series
Sequence recurrence or nth term
nta_pyq_2025_apr
Grade 12
Question:
Let a be the n n th term of an A. P. If S$n =$$a_{1}$$+$$a_{2}$$+ a_{3}$+$\$ldots + an = 700$,$$a_{6}$= 7$and$S = 7$, then a is equal to$: 7 n
Step-by-Step Solution
Key Concept: Use the given$nth-term$relation to derive the required term or ratio from the sequence definition.
...(i) n$S_n = 700$= [$2a +$(n - 1)$d$] 2$(3)$$a_{6} = 7$$\Rightarrow$$a + 5d = 7$...(ii) 7$S_{7} = 7$$\Rightarrow$ ($2a + 6$d) = 7 2$a + 3d = 1$...(iii) Solve (ii) and (iii) n 2 (-$16 + 3n - 3) = 700$$\Rightarrow$$3n - 19n - 1400 = 0$2 ($3n + 56)$(n - 25)$= 0$∴$a_{25} = a + 24$d = -$8 + 24$$\times$ 3 = -$8 + 72 =64$
Correct Answer: 3