model 6 operations of consecutive numbers (odd, even, square, etc.) Section-Wise Topic Notes With Detailed Explanation And Example Questions

Answer: (a)

Series of first 20 odd natural numbers is an arithmetic progression with 1 as the first term and the common difference 2.

Sum of n terms in arithmetic progression is given by.

$S_n =1/2n[2a + (n – 1)d]$

Where a : First term; d : common difference

$S_{20}= 1/2×20[(2×1) + (20 -1) × 2]$

= 10 [2 + 38]=10 × 40 = 400

Note :Sum of first n consecutive odd numbers = $n^2$

Answer: (d)

Series of all natural numbers from 75 to 97 is in A.P. whose first term,

a = 75, last term, l = 97

If number of terms be n, then $a_n$ = a + (n–1)d

97 = 75 + (n – 1)

n = 97 – 74 = 23

$S_n = n/2(a+l)$

$S_23 = 23/2(75+97)$

= $23/2$× 172=1978

Answer: (c)

$10^2 + 11^2 + 12^2$ = 100 + 121 + 144 = 365

Required sum =10 + 11 + 12 = 33

Answer: (a)

Let the numbers be 3x, 3x + 3 and 3x + 6

3x + 3x + 3 + 3x + 6 = 72

9x + 9 = 72

9x = 72 – 9 = 63

x =$63/9$ = 7

∴ Largest number = 3x + 6 = 3 × 7 + 6 = 27

Answer: (d)

Sum of five consecutive integers = S

Third integer = $S/5$

Largest integer = $S/5$ + 2 = ${S+10}/5$

Answer: (d)

S = 1 + 3 + 5 + ..... to 50 terms

Here, a = 1; d = 3 – 1 = 2; n = 50

S = $n/2[2a + (n - 1)d]$

= $50/2[2×1+ (50 - 1) ×2]$

= 25 (2 + 98) = 25 × 100 = 2500