Q30 of 805 Page 1

The first and last terms of an A.P. are 8 and 350 respectively. If it’s common difference is 9, how many terms are there and what is their sum?

OR


How many multiple of 4 lie between 10 and 250? Also find their sum.


Given that a = 8, Tn = 350 and d = 9

To find n and Sn


Tn = a + (n – 1)d = 350


8 + (n – 1)(9) = 350


n = 39


Sn = n/2(2a + (n – 1)d)


= 39/2(2×8 + (39 – 1)9)


= 6981


OR


The first number which is multiple of 4 and greater than 10 is 12 and the second number which is multiple of 4 is 16.


The last number which is less than 250 and multiple of 4 is 248.


It becomes an A.P with first term 12 and common difference 4.


A.P. ⇒ 12, 16, 20, ……, 248


We know, if a and d are first term and common difference of an AP respectively, nth term equals


Tn = a + (n – 1)d


248 = 12 + (n – 1)4


n = 60


Also, sum of first n terms is



= 30(24 + 59×4)


= 7800


More from this chapter

All 805 →
28

Two dice are rolled once. Find the probability of getting such numbers on two dice, whose product is 12.

OR


A box contains 80 discs which are numbered from 1 to 80. If one disc is drawn at random from the box, find the probability that it bears a perfect square number.


 29

Prove that the tangents at any point of a circle is perpendicular to the radius through the point of contact.

 31

A train travels 180 km at a uniform speed. If the speed had been 9 km/hour more, it would have taken 1 hour less for the same journey. Find the speed of the train.

OR


Find the roots of the equation .


 32

In figure 6, three circles each of radius 3.5 cm are drawn in such a way that each of them touches the other two. Find the area enclosed between these three circles (Shaded region). [use

π = 22/7]