Q15 of 47 Page 1

If the sum of first 7 terms of an A.P. is 49 and that of its first 17 terms is 289, find the sum of first n terms of the A.P.

Let us assume the 1st term be a and common differed be d

It is given in the question that,


S7 = 49 and =S17 = 289


We know that, .


∴.


.


2a + 6d = 14 (i)


Also, .


+ 16d = 34 (ii)


Now, by solving (i) and (ii) we get:


-0d = - 20


∴ d = 2


tting the value of d in (i), we get:


2a + 12 = 14


= 2


a = 1


∴



.


.


Hence, Proved


More from this chapter

All 47 →
13

In Fig. 6, ABC is a triangle coordinates of whose vertex A are (0, -1). D and E respectively are the mid-points of the sides AB and AC and their coordinates are (1, 0) and (0, 1) respectively. If F is the mid-point of BC, find the areas of.

 14

In fig. 7, are shown two arcs PAQ and PBQ. Arc PAQ is a part of circle with center O and radius OP while arc PBQ is a semi-circle drawn on PQ as diameter with center M. If OP = PQ = 10 cm, show that area of shaded region is.

 16

Solve for x:

 17

Awell of diameter 4 m is dug 21 m deep. The earth taken out of its has been spread evenly all around it in the shape of a circular ring of width 3 m to form an embankment. Find the height of the embankment.