General term of an A.P., whose first term is 'a' and common difference is 'd' is given by a_n = ..........

1

(a)

a + (n - 1)d

If a, b, c are in A.P., then b = ..........

1

(a)

\(\frac{a + c}{2}\)  [\(\because\) a, b, c are in A.P.  b - a = c - b
\(\Rightarrow\) 2b = a + c
\(\Rightarrow\)  b = \(\frac{a + c}{2}\) ]

In an A.P. the common difference is always ...........

1

(a)

constant

The constant difference between the consecutive terms of an A.P. is called.......

1

(a)

common difference

If there are p terms in an A.P., then nth term form the end is ................ th term.

1

(a)

p - n + 1

What is the next term of an AP.\( \sqrt { 7 } ,\sqrt { 28 } ,\sqrt { 63 } ,.....?\)

1

(a)

Here, 
\(a=\sqrt { 7 } ,a+d=\sqrt { 28 } \)
\(d=\sqrt { 28 } -\sqrt { 7 } =2\sqrt { 7 } -\sqrt { 7 } \)
\(=\sqrt { 7 } \)
\(\Rightarrow Next\quad term=\sqrt { 7 } +(4-1)\sqrt { 7 } \)
\(\Rightarrow =\sqrt { 7 } (4)\)
\(\Rightarrow =\sqrt { 7\times 16 } \)
\(=\sqrt { 112 } \)

Find the 25^th term of the AP. \(-5,-\frac{5}{2}, 0, \frac{5}{2}\)...............

1

(a)

a = - 5, d = - 5 / 2- (-5) = 5 / 2
n^th term = a + (n-1) d
25^th term = - 5 + (25 - 1) (5 / 2)
= - 5 + 60
= 55

In the A.P. 2, x, 26 find the value of x.

1

(a)

2, x and 26 are in A.P.
\(\therefore\)x-2 = 26-x
\(\Rightarrow\) 2x=26+2
\(\Rightarrow\) x = 28/2 = 14

If 18, a, b, - 3 are in A.P.,then find a + b.

1

(a)

Since 18, a, b, and - 3 are in A.P., Then
a-18 = -3-b
\(\Rightarrow\)a + b = - 3 + 18 -
\(\Rightarrow\) a + b = 15 

What is the sum of five positive integers divisible by 6.

1

(a)

Here, a = 6, d = 6, n = 5
\(\because\) S = n/2[2a+(n-l)d]
S₅ = 5/2[2x6+(5-1)(6)]
= 5/2[12+4x6]
= 5/2[12+24] = 5/2[36]
= 5x18 = 90

If nth term of an A.P. is 6n + 2, then common difference is 6.

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(a) False

(b) True

List of number of students left in the school auditorium from to total strength of 1250 students when they leave the auditorium in batches of 25, form an A.P.

1

(a) False

(b) True

List of numbers 2, 4, 8, 16, ......, form an A.P.

1

(a) True

(b) False

The sum of first 100 natural numbers are 10100.

1

(a) True

(b) False

The sum of first 4 terms and sum of first 13 terms of the A.P. 24, 21, 18, .......... is 78.

1

(a) True

(b) False

Write down the first four terms of the sequences whose general terms are T_n = 2n + 3

1

(a)

T_n = 2n + 3
T₁ = 2 x 1 + 3 =5,
T₂ = 2 x 2 + 3 = 7,
T₃ = 2 x 3 + 3 = 9,
T₄ = 2 x 4 + 3 = 11
Ist four terms are 5, 7, 9 and 11.

Write down the first four terms of the sequences whose general terms are T_n = 3ⁿ⁺¹

1

(a)

T_n = 3ⁿ⁺¹ 
T₁ = 3¹⁺¹ = 9,
T₂ = 3²⁺¹ = 27,
T₃ = 3³⁺¹ = 81,
T₄ = 3⁴⁺¹ = 243
Ist four terms are 9, 27, 81 and 243.

Write down the first four terms of the sequences whose general terms are T₁ = 2, T_n = T_n-1 + 5, n \(\ge \) 2

1

(a)

T₁ = 2, T_n = T_n-1 + 5, n \(\ge \) 2
T₂ = T_2-1 + 5 = T₁ + 5 = 2 + 5 = 7
T₃ = T_3-1 + 5 = T₂ + 5 = 7 + 5 = 12
T₄ = T_4-1 + 5 = T₃ + 5 = 12 + 5 = 17
Ist four terms are 2, 7, 12 and 17.

Find the 8th term of 117, 104, 91, 78,...

1

(a)

a = 117,
d = 104 - 117 = -13
a₈ = a + 7d = 117 + 7 x (-13) = 26

Find the 10th term of 10.0, 10.5, 11.0, 11.5,...

1

(a)

a = 10,
d = 10.5 - 10 = 0.5
a₁₀ = a + 9d = 10 + 9 x 0.5 = 14.5