First slide

Arithmetic progression

Question

The sum of all two digit numbers which when divided by 4, yield unity as remainder, is

Moderate

A

1100
B

1200
C

1210
D

None of these

Solution

The first two digit number which when divided by 4 leaves remainder 1 is 4 .3 + 1 = 13 and last is 4 . 24 + 1 = 97.
Thus, we have to find the sum
$13 + 17 + 21 + \dots + 97$
which is an A.P.
$∴ 97 = 13 + (n - 1) \cdot 4 \Rightarrow n = 22$
$\begin{aligned} and S_{n} = \frac{n}{2} [a + l] = 11 \times [13 + 97] \\ = 11 \times 110 = 1210 . \end{aligned}$

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