SSC (Marathi Semi-English) १० वीं कक्षा - Maharashtra State Board Question Bank Solutions for Algebra Mathematics 1

If the sum of first p terms of an A.P. is equal to the sum of first q terms then show that the sum of its first (p + q) terms is zero. (p ≠ q)

If m times the m^th term of an A.P. is eqaul to n times n^th term then show that the (m + n)^th term of the A.P. is zero.

Rs 1000 is invested at 10 percent simple interest. Check at the end of every year if the total interest amount is in A.P. If this is an A.P. then find interest amount after 20 years. For this complete the following activity.

The first term of an A. P. is 5 and the common difference is 4. Complete the following activity and find the sum of the first 12 terms of the A. P.

a = 5, d = 4, s12 = ?
`s_n = n/2 [ square ]`
`s_12 = 12/2 [10 +square]`
         `= 6 × square  `
         ` =square`

There are 25 rows of seats in an auditorium. The first row is of 20 seats, the second of 22 seats, the third of 24 seats, and so on. How many chairs are there in the 21st row ?

Find out the sum of all natural numbers between 1 and 145 which are divisible by 4.

Simplify `sqrt(50)`

What is the sum of first 10 terms of the A. P. 15,10,5,........?

Fill up the boxes and find out the number of terms in the A.P.
1,3,5,....,149 .

Here a = 1 , d =b`[    ], t_n = 149`

t_n = a + (n-1) d 

∴ 149 =`[  ]     ∴149 = 2n -  [  ]`
∴ n =`[  ]`

The sum of third and seventh term of an A. P. is 6 and their product is 8. Find the first term and the common difference of the A. P. 

Solve the quadratic equation 2x² + 5x + 2 = 0 using formula method.

Obtain the sum of the first 56 terms of an A.P. whose 18^th and 39^th terms are 52 and 148 respectively.

Obtain the sum of the first 56 terms of an A.P. whose 18^th and 39^th terms are 52 and 148 respectively.

Find second and third terms of an A.P. whose first term is – 2 and the common difference is – 2.

In an A.P. sum of three consecutive terms is 27 and their products is 504. Find the terms. (Assume that three consecutive terms in an A.P. are a – d, a, a + d.)

Complete the following activity to solve the given quadratic equation by formula method.

2x² + 13x + 15 = 0

Activity: 2x² + 13x + 15 = 0

a = (______), b = 13, c = 15

b² – 4ac = (13)² – 4 × 2 × (______)

= 169 – 120

b² – 4ac = 49

x = `(-"b" +- sqrt("b"^2 - 4"ac"))/(2"a")`

x = `(- ("______") +- sqrt(49))/4` 

x = `(-13 +- ("______"))/4`

x = `(-6)/4` or x = `(-20)/4`

x = (______) or x = (______)

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

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