Question

if the sum of 1st 7 and 15 terms of an AP are 98 and 390 find the sum of 1st 10 terms

Answer 1

HELLO DEAR,


given that:-

s₇= 98

=> s₇ = 7/2 [ 2a + (7-1)d ] = 98

=> 196 = 7(2a +6d)

=> 28 = 2a + 6d

=> a + 3d = 14 --------------(1)


and

s₁₅ = 390

=> s₁₅ = 15/2[ 2a + (15-1)d] = 390

=> 780 = 15(2a + 14d)

=> 52 = 2a + 14d

=> a + 7d = 26------------(2)


from --(1) and --(2)


a + 3d = 14
a + 7d = 26
(-)__(-)__(-)
————————
-4d = -12


=> d =3 put in --(1)

we get,

a + 3(3) = 14

=> a = 14 - 12

=> a = 2


NOW,


a₁₀ = a + ( 10 - 1) ×d

=> 2 + 9×3

=> 29



I HOPE ITS HELP YOU DEAR,
THANKS