# In an AP i)given a=7,a13=35, find d and S13. ii)given a3=15,S10=125,find d and a10.

1
by rajnani
ya its crct
that is a or a3??
a3
yup i m doing got it
carry on !!!

2015-05-08T16:20:11+05:30
i) given a=7, a13=35
a13 (or)  a+12d = 35 ------- 1
a = 7 (or) a+0d = 7  ------- 2
by subtracting 1 with 2 we get

a+12d = 35
a+  0d = 07
-       -      -
------------------
12d = 28
-------------------
d = 28/12 = 2.33
so,  d = 2 (approximately)

S13 = n/2 [a+l]
n=13, a= 7, a13 = l = 35
S13 = 13/2 [7+35]
S13 = 13/2 [42]
S13 = 13 [21]
therefore, S13 = 273

ii) S10 = 125, a3 = 15 is given
S10 = 125 = 10/2 (2a+9d)     [since  a+l means a+a10 = a+a+9d]
2a+9d=25 ------- 1
a3 = a+2d = 15 ------ 2
subtracting 2 from 1 we get,
2a+9d-(a+2d) = 25-15
a+7d=10
i.e., a8 = 10   and given a3=15

subtracting a3 from a8 we get
(a+7d)-(a+2d) = 10-15
5d=-5
d = -1
by keeping it in 2 we get
a+2(-1) = 15
a= 15+2
a= 17
then,
a10 = a+9d = 17+9(-1) = 17-9 = 8
therefore,
a10 = 8

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