On the world environment day tree plantation programme was arranged on a land which is triangular in shape. Trees are planted such that in the first row there is one tree, in the second row there are two trees, in the third row three trees and so on. Find the total number of trees in the 25 rows.

First term a = 1Second term t1 = 2Third term t3 = 3Common difference d = t3 – t2 = 3 – 2 = 1We need to find total number of trees when n = 25Thus, by using sum of nth term of an A.P. we will find its sum Where, n = no. of termsa = first termd = […]

Kargil’s temperature was recorded in a week from Monday to Saturday. All readings were in A.P. The sum of temperatures of Monday and Saturday was 5° C more than sum of temperatures of Tuesday and Saturday. If temperature of Wednesday was – 30° Celsius then find the temperature on the other five days.

Let Monday be the first term i.e. a = t1Let Tuesday be the second term that is t2Let Wednesday be the third term that is t3Let Thursday be the fourth term that is t4Let Friday be the fifth term that is t5Let Saturday be the sixth term that is t6Given: t1 + t6 = 5 + (t2 + […]

There is an auditorium with 27 rows of seats. There are 20 seats in the first row, 22 seats in the second row, 24 seats in the third row and so on. Find the number of seats in the 15th row and also find how many total seats are there in the auditorium?

Given first term a = 20Second term t1 = 22Third term t2 = 24Common difference d = t2 – t1 = 24 – 22 = 2We need to find t15 thus n = 15Now, by using nth term of an A.P. formulatn = a + (n – 1) dwhere n = number of termsa = first termd = common differencetn = nth termsOn substituting […]

Sachin invested ina national saving certificate scheme. In the first year he invested ₹ 5000, in the second year ₹ 7000, in the third year ₹ 9000 and so on. Find the total amount that he invested in 12 years.

According to the question we can form an A.P.5000, 7000, 9000, ……Hence, the first term a = 5000Second term t1 = 7000Third term t2 = 9000Thus, common difference d = t2 – t1 = 9000 – 7000 = 2000Here, number of terms n = 12We need to find S12Now, by using sum of nth term of an A.P. we will […]

A man borrows ₹ 8000 and agrees to repay with a total interest of ₹ 1360 in 12 monthly instalments. Each instalment being less than the preceding one by ₹ 40. Find the amount of the first and last instalment.

Given A man borrows = Rs. 8000Repay with total interest = Rs 1360In 12 months, thus n = 12Thus, S12 = 8000 + 1360 = 9360Each installment being less than preceding oneThus, d = – 40We need to find “a”Now, by using sum of nth term of an A.P. we will find its sum Thus, last installment […]