Balbharati solutions for Algebra (Mathematics 1) [English] 10 Standard SSC Maharashtra State Board chapter 3 - Arithmetic Progression [Latest edition]

Which of the following sequences are A.P.? If they are A.P. find the common difference.

2, 4, 6, 8, ...

Which of the following sequences are A.P.? If they are A.P. find the common difference.

Which of the following sequences are A.P.? If they are A.P. find the common difference.

–10, –6, –2, 2,...

Is the following sequences are A.P.? If is A.P. find the common difference.

0.3, 0.33, 0.333,...

Is the following sequences are A.P.? If is A.P. find the common difference.

0, –4, –8, –12,...

Is the following sequences are A.P.? If is A.P. find the common difference.

Which of the following sequences are A.P.? If they are A.P. find the common difference.

`3, 3 + sqrt2, 3 + 2sqrt2, 3 + 3sqrt2, ...`

Which of the following sequences are A.P. ? If they are A.P. find the common difference .

127, 132, 137,...

Write an A.P. whose first term is a and the common difference is d in the following.

a = 10, d = 5 

Write an A.P. whose first term is a and common difference is d in the following.

a = –3, d = 0

Write an A.P. whose first term is a and common difference is d in the following.

Write an A.P. whose first term is a and common difference is d in the following.

a = –1.25, d = 3 

Write an A.P. whose first term is a and common difference is d in  the following.

a = 6, d = –3 

Write an A.P. whose first term is a and common difference is d in the following.

a = –19, d = –4

Find the first term and common difference for  the A.P. 

5, 1, –3, –7,...

Find the first term and common difference for  the A.P.

0.6, 0.9, 1.2,1.5,...

Find the first term and common difference for  the A.P.

127, 135, 143, 151,...

Find the first term and common difference for the A.P.

`1/4,3/4,5/4,7/4,...`

Write the correct number in the given boxes from the following A. P.

1, 8, 15, 22,... 
Here a =Here a = t₁ = , t₂ = , t₃ = ,

t₂ – t₁ = – =
t₃ – t₂ = – =  ∴ d =

Write the correct number in the given boxes from the following A. P.

3, 6, 9, 12,...

Here  t₁ =  t₂ = , t₃ = , t₄ = ,
t₂ – t₁ = , t₃ – t₂ =    ∴ d =

Write the correct number in the given boxes from the following A. P.

–3, –8, –13, –18,... 

Here  t₃ = , t₂ = , t₄ =, t₁ = ,
t₂ – t₁ = , t₃ – t₂ =    ∴ a = , d =

Write the correct number in the given boxes from the following A. P.

70, 60, 50, 40,... 
Here  t₁ = , t₂ = , t₃ = ,...
∴ a = , d =

Decide whether the following sequence is an A.P., if so find the 20^th term of the progression:

–12, –5, 2, 9, 16, 23, 30, ..............

Find the 19^th term of the following A.P.:

7, 13, 19, 25, ...

Find the 27^th term of the following A.P.
9, 4, –1, –6, –11,...

Find how many three digit natural numbers are divisible by 5.

The 11^th term and the 21^st term of an A.P. are 16 and 29 respectively, then find the 41^th term of that A.P.

First term and the common differences of an A.P. are 6 and 3 respectively; find S₂₇.

Solution: First term = a = 6, common difference = d = 3, S₂₇ = ?

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

S_n = `27/2 [12 + (27 - 1)square]`

= `27/2 xx square`

= 27 × 45

S₂₇ = `square`

Find the sum of first 123 even natural numbers.

Complete the following activity to find the sum of natural numbers from 1 to 140 which are divisible by 4. 

Sum of numbers from 1 to 140, which are divisible by 4 = `square`

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

Find four consecutive terms in an A.P. whose sum is 12 and sum of 3^rd and 4^th term is 14.

(Assume the four consecutive terms in A.P. are a – d, a, a + d, a +2d) 

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

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

Choose the correct alternative answer for  the following question .
The sequence –10, –6, –2, 2,...

Choose the correct alternative answer for  the following question .

First four terms of an A.P. are ....., whose first term is –2 and common difference is –2.

Choose the correct alternative answer for  the following question .

 What is the sum of the first 30 natural numbers ?

For an given A.P., t₇ = 4, d = −4, then a = ______.

Choose the correct alternative answer for the following question.

For an given A.P. a = 3.5, d = 0, n = 101, then t_n = ....

Choose the correct alternative answer for  the following question . 

In an A.P. first two terms are –3, 4 then 21^st term is ...

Choose the correct alternative answer for  the following question .

 If for any A.P. d = 5 then t₁₈ – t₁₃ = .... 

The Sum of first five multiples of 3 is ______.

Choose the correct alternative answer for  the following question .

15, 10, 5,... In this A.P sum of first 10 terms is...

Choose the correct alternative answer for  the following question .

 In an A.P. 1^st term is 1 and the last term is 20. The sum of all terms is = 399 then n = ....

Find the fourth term from the end in an A.P. –11, –8, –5,...., 49.

In an A.P. the 10^th term is 46 sum of the 5^th and 7^th term is 52. Find the A.P.

The A.P. in which 4^th term is –15 and 9^th term is –30. Find the sum of the first 10 numbers.

Two A.P.’ s are given 9, 7, 5, . . . and 24, 21, 18, . . . . If n^th term of both the progressions are equal then find the value of n and n^th term.

If sum of 3^rd and 8^th terms of an A.P. is 7 and sum of 7^th and 14^th terms is –3 then find the 10^th term.

Divide 207 in three parts, such that all parts are in A.P. and product of two smaller parts will be 4623.

There are 37 terms in an A.P., the sum of three terms placed exactly at the middle is 225 and the sum of last three terms is 429. Write the A.P.

If first term of an A.P. is a, second term is b and last term is c, then show that sum of all terms is  \[\frac{\left( a + c \right) \left( b + c - 2a \right)}{2\left( b - a \right)}\].

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.