Arithmetic Progression - For arithemetic progression addition of first 17 terms is 24 and addition of first 24 terms is 17 , then find addition of fir ... calculator

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Arithmetic Progression

8. For arithemetic progression addition of first 17 terms is 24 and addition of first 24 terms is 17 , then find addition of first 41 terms.

We know that,

$S_n = n/2 [2a + (n - 1)d]$

$S_17 = 17/2 * [2a + (17 - 1)d] = 24$

$=> 17/2 * [2a + 16d] = 24$

$=> 2a + 16 d = 2.8235 ->(1)$

We know that,

$S_n = n/2 [2a + (n - 1)d]$

$S_24 = 24/2 * [2a + (24 - 1)d] = 17$

$=> 24/2 * [a + 23d] = 17$

$=> 2a + 23d = 1.4167 ->(2)$

Solving

$7 d = -1.4069$

$=> d = -0.201$

From

$(1) => 2a + 16d = 2.8235$

$=> 2a = 2.8235 - 16d$

$=> 2a = 2.8235 - 16 × -0.201$

$=> 2a = 2.8235 - -3.2157$

$=> 2a = 6.0392$

$=> a = 3.0196$

We know that,

$S_n = n/2 [2a + (n - 1)d]$

$:. S_41 = 41/2 * [2(3.0196) + (41 - 1)(-0.201)]$

$= 41/2 * [6.0392 + (-8.0392)]$

$= 41/2 × -2$

$= -41$