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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.

241 Views

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?

Original cost of scooter = Rs. 22000

Amount paid in cash = Rs. 4000

Amount to be paid in instalments = Rs. 18000

Let a denote the first instalment

a = 1000 + 10% interest on unpaid amount

= Rs . $left square bracket 1000 space plus space 10 over 100 cross times 18000 right square bracket space equals space Rs. space left square bracket 1000 space plus space 1800 right square bracket space equals space Rs. space 2800$

$rightwards double arrow$ a = Rs. 2800

2nd instalment = $space space 1000 space plus space 10 over 100 cross times 17000 space equals space 1000 plus 1700 space equals space space Rs. space 2700$

Similarly, 3rd instalment = Rs. 2600

∴ Various instalments are Rs. 2800, Rs. 2700, Rs. 2600.........

Amount paid in instalments = Rs. 2800 + Rs . 2700 + Rs . 2600 + ......+ Rs. 1100

= Rs . $space space 18 over 2 left square bracket 2 left parenthesis 2800 right parenthesis space plus space left parenthesis 18 minus 1 right parenthesis left parenthesis negative 100 right parenthesis right square bracket$

$open square brackets table row cell because space space space space space space space a equals space 2800 comma space d space equals space 2700 space minus 2800 space equals space minus 100 comma end cell row cell U sin g space S subscript n space equals space n over 2 left square bracket 2 a plus left parenthesis n minus 1 right parenthesis d end cell end table close square brackets$

= Rs. 9[5600 - 1700] = Rs. 9(3900) = Rs. 35100

Actual amount by Hari = Rs. [35100 + 4000] = Rs 39100

336 Views

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.

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