QQuestion
Which term of the Arithmetic Progression 15, 30, 45, 60, … is 300? Hence, find the sum of all the terms of the A.P. up to 300.
ICSEClass 10Mathematics03 Mark2023 Easy
✓Answer
Given A.P.: 15, 30, 45, 60, …
First term, a = 15
Common difference, d = 30 − 15 = 15
Let the nth term be 300.
⇒ aₙ = a + (n − 1)d
⇒ 300 = 15 + (n − 1)15
⇒ 300 = 15 + 15n − 15
⇒ 300 = 15n
⇒ n = \frac{300}{15}
⇒ n = 20
Therefore, 300 is the 20th term.
Now,
⇒ Sₙ = \frac{n}{2}(a + aₙ)
⇒ S₂₀ = \frac{20}{2}(15 + 300)
⇒ S₂₀ = 10 × 315
⇒ S₂₀ = 3150
Therefore, the sum of all terms up to 300 is 3150.
Was this answer helpful?
Related Questions
More ICSE Easy level questions
1/12
The fourth term of a Geometric Progression (G.P.) is 16 and its seventh term is 128. Find its: (a) common ratio (b) first term
Rohit and Vinay both opened a recurring deposit account in a bank for 2 years at 8% simple interest. Vinay deposited ₹ 300 per month. On maturity, Rohit’s interest was ₹ 800 more than Vinay’s interest. Find: (a) interest earned by Vinay. (b) sum deposited by Rohit every month.
Kabir bought 120 shares of a company with nominal value ₹100, available at a premium of ₹25. Find: (a) the money invested by Kabir in buying these shares. (b) the rate of dividend, if he received ₹1,080 as dividend from these shares after one year. (c) his rate of return.
If x = , a ≠ b, (a) Find: (b) Using properties of proportion, find:
Solve the following inequation, write the solution set and represent it on the real number line. −1 < − ≤ 1, x ∈ R
A survey was conducted on 300 families having 2 children each. The results obtained are given below. Number of girl child Number of families 2 95 1 165 0 40 Total 300 If one family is selected at random, find the probability that it will have: (a) one girl child (b) one or more girl child (c) no boy child
Use the following graph and answer the given questions : (a) Write the co-ordinates of points A, B and C. (b) Find the equation of a line passing through the mid-point of AC and parallel to AB.
Find the mean of the following frequency distribution using step-deviation method. Take assumed mean = 28. Class interval Frequency 0–8 10 8–16 20 16–24 14 24–32 16 32–40 18 40–48 22
Asha buys ₹ 20 shares of a company which pays 9% dividend at such a price that she gets a return of 12% on her investment. At what price did she buy each share? (a) ₹ 20 (b) ₹ 15 (c) ₹ 25 (d) ₹ 18
If A = , then A² is equal to: (a) (b) (c) (d)
Statement 1: The point which is equidistant from three non-collinear points D, E and F is the circumcentre of △DEF. Statement 2: The incentre of a triangle is the point where the bisectors of the angles intersect. (a) Both statements are true. (b) Both statements are false. (c) Statement 1 is true and Statement 2 is false. (d) Statement 1 is false and Statement 2 is true.
(x + 3), 1, (3x − 7) and −5 are in proportion. The value of x is : (a) −1 (b) 1 (c) −5 (d) 5