SSC (English Medium) इयत्ता १० वी - Maharashtra State Board Question Bank Solutions for Algebra

Find the sum of first 1000 positive integers.

Activity :- Let 1 + 2 + 3 + ........ + 1000

Using formula for the sum of first n terms of an A.P.,

S_n = `square`

S₁₀₀₀ = `square/2 (1 + 1000)`

= 500 × 1001

= `square`

Therefore, Sum of the first 1000 positive integer is `square`

For an A.P., If t₁ = 1 and t_n = 149 then find S_n.

Activitry :- Here t₁= 1, t_n = 149, S_n = ?

S_n = `"n"/2 (square + square)`

= `"n"/2 xx square`

= `square` n, where n = 75

In an A.P. a = 2 and d = 3, then find S₁₂

If a = 6 and d = 10, then find S₁₀ 

Determine the sum of first 100 terms of given A.P. 12, 14, 16, 18, 20, ......

Activity :- Here, a = 12, d = `square`, n = 100, S₁₀₀ = ?

S_n = `"n"/2 [square + ("n" - 1)"d"]`

S₁₀₀ = `square/2 [24 + (100 - 1)"d"]`

= `50(24 + square)`

= `square`

= `square`

Find the sum of natural numbers between 1 to 140, which are divisible by 4.

Activity: Natural numbers between 1 to 140 divisible by 4 are, 4, 8, 12, 16,......, 136

Here d = 4, therefore this sequence is an A.P.

a = 4, d = 4, t_n = 136, S_n = ?

t_n = a + (n – 1)d

`square` = 4 + (n – 1) × 4

`square` = (n – 1) × 4

n = `square`

Now,

S_n = `"n"/2["a" + "t"_"n"]`

S_n = 17 × `square`

S_n = `square`

Therefore, the sum of natural numbers between 1 to 140, which are divisible by 4 is `square`.

Find S₁₀ if a = 6 and d = 3

Find the sum of three-digit natural numbers, which are divisible by 4

What is the sum of an odd numbers between 1 to 50?

Find the sum of numbers between 1 to 140, divisible by 4

In a ‘Mahila Bachat Gat’, Sharvari invested ₹ 2 on first day, ₹ 4 on second day and ₹ 6 on third day. If she saves like this, then what would be her total savings in the month of February 2010?

Find the sum of odd natural numbers from 1 to 101

Shubhankar invested in a national savings certificate scheme. In the first year he invested ₹ 500, in the second year ₹ 700, in the third year ₹ 900 and so on. Find the total amount that he invested in 12 years

A merchant borrows ₹ 1000 and agrees to repay its interest ₹ 140 with principal in 12 monthly instalments. Each instalment being less than the preceding one by ₹ 10. Find the amount of the first instalment

Find t₂₁, if S₄₁ = 4510 in an A.P.

If ₹ 3900 will have to be repaid in 12 monthly instalments such that each instalment being more than the preceding one by ₹ 10, then find the amount of the first and last instalment

Find the next 4 terms of the sequence `1/6, 1/4, 1/3`. Also find S_n.

Complete the following activity to find the 19^th term of an A.P. 7, 13, 19, 25, ........ :

Activity: 

Given A.P. : 7, 13, 19, 25, ..........

Here first term a = 7; t₁₉ = ?

t_n + a + `(square)`d .........(formula)

∴ t₁₉ = 7 + (19 – 1) `square`

∴ t₁₉ = 7 + `square`

∴ t₁₉ = `square`

Find the sum of first 'n' even natural numbers.

Measures of angles of a triangle are in A.P. The measure of smallest angle is five times of common difference. Find the measures of all angles of a triangle. (Assume the measures of angles as a, a + d, a + 2d)