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Question
Sum of all two digit numbers which when divided by 4 yield unity as remainder is
Options
1200
1210
1250
none of these.
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Solution
1210
The given series is 13, 17, 21....97.
\[a_1 = 13, a_2 = 17, a_n = 97\]
\[d = a_2 - a_1 = 7 - 3 = 4\]
\[a_n = 97\]
\[ \Rightarrow a + \left( n - 1 \right)d = 97\]
\[ \Rightarrow 13 + \left( n - 1 \right)4 = 97\]
\[ \Rightarrow n = 22\]
Sum of the above series:
\[S_{22} = \frac{22}{2}\left\{ 2 \times 13 + \left( 22 - 1 \right)4 \right\}\]
\[ = 11\left\{ 26 + 84 \right\}\]
\[ = 1210\]
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