Question

An Arithmetic progression has 3 as its terms. Also the sum of 8 terms is twice as sum of first 5 terms.
Find common difference

Answer 1

10th to 99th, any table,
very easy method to learn.
I didn't know this.

How to write Table of any two digit number?

F*or example Table of *87*

First write down *table of 8 then write down table of 7 beside it*

8 7 87
16 14 (16+1) 174
24 21 (24+2) 261
32 28 (32+2) 348
40 35 (40+3) 435
48 42 (48+4) 522
56 49 (56+4) 609
64 56 (64+5) 696
72 63 (72+6) 783
80 70 (80+7) 870

Now table of 38

3 8 38
6 16 (6+1) 76
9 24 (9+2) 114
12 32 (12+3) 152
15 40 (15+4) 190
18 48 (18+4) 228
21 56 (21+5) 266
24 64 (24+6) 304
27 72 (27+7) 342
30 80 (30+8) 380
33 88 (33+8) 418
36 96 (36+9) 456

Now table of 92

9 2 92
18 4 184
27 6 276
36 8 368
45 10 (45+1)460
54 12 (54+1)552
63 14 (63+1)644
72 16 (72+1)736
81 18 (81+1)828
90 20 (90+2)920
99 22 (99+1)1012
108 24 (108+2)1104

This way one can make Tables from 10

This is Vedic Mathematics!!..

Answer 2

According to the first condition
3= a / t1
According to the second condition
S 8 = 2 (S 5)
Sn = n/2 [ 2a ( n-1) d]
S 8 = 8/2 [ 2 (3) (8-1) d]
S8 = 4 [ 6 (7) d]
S8= 4 [ 42 d]
S8 = 168d
S5 = 5/2 [ 2 (3) ( 5-1) d]
S5 = 5/2 [ 6 (6) d]
S5 = 5/2 [ 36 d]