First slide

Arithmetic progression

Question

A student read common difference of an A.P as -3 instead of 3 and obtained the sum of first 10 terms -30. Then, the actual sum of first 10 terms is equal to

Moderate

A

240
B

120
C

300
D

180

Solution

Let common difference $d_{1} = - 3$ and first term be $a$ .
$∴$    Series become $a, a - 3, a - 6, ..., a - 27$

$∴ S = 10 a + (- 3 - 6 - ... - 27)$

$\Rightarrow - 30 = 10 a - 3 (1 + 2 + .... + 9)$

$\Rightarrow - 30 = 10 a - 3 [\frac{9 (9 + 1)}{2}]$

$\Rightarrow - 30 = 10 a - 135$

$\Rightarrow 10 a = 105$

$\Rightarrow a = \frac{105}{10}$

Now, correct common difference $d_{2} = 3$

$∴$ Required sum $= \frac{10}{2} [2 \times \frac{105}{10} + (10 - 1) 3]$

                                $= 5 [\frac{105}{5} + 27]$

                               $= 5 \times 48 = 240$

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