Question

The number of terms of the A.P. 3,7,11,15...to be taken so that the sum is 406 is.

• A. 5
• B. 10
• C. 12
• D. 14

Answer 1

Answer: (D)

14

Answer 2

$S = \frac { n } { 2 } [ 2 a + ( n - 1 ) d ]$

⇒ $406 = \frac { n } { 2 } [ 6 + ( n - 1 ) 4 ]$ ⇒ $812 = n [ 6 + 4 n - 4 ]$

⇒ $812 = 2 n + 4 n ^ { 2 }$ ⇒ $406 = 2 n ^ { 2 } + n$

⇒ $2 n ^ { 2 } + n - 406 = 0$

⇒ $n = \frac { - 1 \pm \sqrt { 1 + 4.2 .406 } } { 2.2 }$ $= \frac { - 1 \pm \sqrt { 3249 } } { 4 }$ $= \frac { - 1 \pm 57 } { 4 }$

Taking (+) sign, $n = \frac { - 1 + 57 } { 4 } = 14$.