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Sequences and Series

Short Answer Type

131. Find the sum to n terms of the following series.

space space space 1 cross times 2 cross times 3 plus 2 cross times 3 cross times 4 plus 3 cross times 4 cross times 5 plus........

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132. Find the sum of n terms of the series 3 + 7 + 13 + 21 + 31 +.......

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133. The ages of the students in a class form an A.P. whose common difference is 4 months. If the youngest student is 8 years old and the sum of the ages of all the students in the class is 168 years. Find the numbers of students in the class.

787 Views

134.

A man deposited Rs. 10,000 in a bank at the rate of 5% simple interest annually. Find the amount in 15th year since he deposited the amount and also calculate the total amount after 20 years.

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135. An insect starts from a point and travels in a straight path 1 mm in the first second and half of the distance covered in the previous second in the succeeding second. In what time would it reach a point 3 mm away from its starting point?

234 Views

136. The interior angles of a polygon are in A.P. The smallest angle is 120° and the common difference is 5°. Find the number of sides of the polygon.

270 Views

Long Answer Type

137. Shamshad Ali buys a scooter for Rs 22000. He pays Rs. 4000 cash and agrees to pay the balance in annual instalment of Rs 1000 plus 10% interest on the unpaid amount. How much will the scooter cost him?

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Short Answer Type

138. A man buys every year Bank’s cash certificates of value exceeding the last year purchase by Rs. 25. After 20 years, he finds that the total value of the certificates purchased by him is Rs. 7250. Find the values of the certificates purchased by him

(i) In the first year. (ii) In the 13th year.

Let Rs. a be the value of the certificates purchased by him in the first year and Rs. d be the value of the certificate in excess every year.

∴ d = Rs. 25

Since the value of the certificates purchased by him after 20 years = 7250

∴ $straight S subscript 20 space equals space 7250$

$rightwards double arrow$ $20 over 2 left square bracket 2 left parenthesis straight a right parenthesis space plus space left parenthesis 20 minus 1 right parenthesis 25 right square bracket space equals space 7250$
$open curly brackets By space using space straight S subscript straight n space equals space straight n over 2 left parenthesis 2 straight a plus top enclose straight n minus 1 end enclose straight d close curly brackets$

$space space space rightwards double arrow space space space space space space space space space 10 left square bracket 2 straight a space plus space 475 right square bracket space space equals space 7250$

$rightwards double arrow$ 2a + 475 = 725 $rightwards double arrow$ 2a = 250 $rightwards double arrow$ a = Rs. 125

∴ Value of the certificates purchased by him in the first year = Rs. 125 New line Value of the certificates purchased by him in the 13th year = a + (13 - 1)d = 125 + 12(25) = Rs. 425

179 Views

Long Answer Type

139. An odd number of stones lie along a straight path, the distance between any two consecutive stones being 10 m. The stones are to the collected at the place where the middle stone lies. A man can carry only one stone at a time. He starts carrying the stones beginning from the extreme stone. If he covers a path of 3 km, how many stones are there ?

183 Views

Short Answer Type

140. The income of a person is Rs. 3,00,000 in first year and he receives an increase of Rs. 10,000 to his income per year for next 19 years. Find the total amount, he received in 20 years.

126 Views