CAT 2025 Slot 3 QA Question 6: In an arithmetic progression, if the sum of fourth, seventh and tenth terms is 99, and the sum of the first fourteen terms is 497, then the sum of first five terms is

Question

In an arithmetic progression, if the sum of fourth, seventh and tenth terms is 99, and the sum of the first fourteen terms is 497, then the sum of first five terms is

Accepted Answer

Let the first term be $a$ and the common difference be $d$.
$(a + 3d) + (a + 6d) + (a + 9d) = 99$
$3a + 18d = 99$
$a + 6d = 33$
$S_{14} = 7(2a + 13d) = 497$
$2a + 13d = 71$
Doubling $a + 6d = 33$ gives $2a + 12d = 66$. Therefore, $d = 5$ and $a = 3$.
$S_5 = \dfrac{5}{2} 	imes (2a + 4d)$
$S_5 = 5(a