Question

निम्नलिखित समांतर श्रेढि़यों में, रिक्त खानों के पदों को ज्ञात कीजिए:
I. 2, ..... , 26
II. .....,13,..... , 3
III. 5,..... ,..... ,$9 \frac{1}{2}$
IV. – 4,.... ,.... , ..... ,.....,6
V. ....,38, ...... , ..... ,....., – 22

Answer 1

I. 2, ..... , 26
यदि तीन पद A.P में दिया गया हो तब मध्य पद , प्रथम और तृतीय पद का औसत होता है ।
अर्थात, मध्य पद = (2 + 26)/2 = 14
यानी , 2 , 14 , 26

II. .....,13,..... , 3
यहाँ , a = ?, a + d = 13 , a + 2d = ? , a + 3d = 3
इसीलिए, a + d = 13 , a + 3d = 3 को हल करते हैं ।
d = -5 तब , a = 18 , a + 2d = 8
यानी , 18, 13, 8, 3

III. 5,..... ,..... ,$9 \frac{1}{2}$
a = 5, a + d = ?, a + 2d = ? , a + 3d = 9½
a + 3d = 9½
5 + 3d = 19/2
3d = 9/2
d = 3/2
इसीलिए, a + d = 5 + 3/2 = 13/2
a + 2d = 5 + 6/2 = 8
यानि, 5, 13/2 , 8 , 9½

IV. – 4,.... ,.... , ..... ,.....,6
a = -4 , a + d = ?, a + 2d = ? , a + 3d = ? a + 4d = ?, a + 5d = 6
a + 5d = 6
-4 + 5d = 6
d = 2 ,
अब, a + d = -4 + 2 = -2
a + 2d = -4 + 4 = 0
a + 3d = -4 + 3 × 2 = 2
a + 4d = -4 + 4 × 2 = -4 + 8 = 4
यानि, -4, -2, 0, 2 , 4, 6

V. ....,38, ...... , ..... ,....., – 22
a = ?, a + d = 38, a + 2d = ?, a + 3d = ?, a + 4d = ?, a + 5d = -22
a + 5d = -22
a + d = 38
4d = -60 => d = -15
a = 53
a + 2d = 53 - 30 = 23
a + 3d = 53 - 45 = 8
a + 4d = 53 - 60 = -7
यानि, 53, 38, 23, 8, -7, -22