Question

Given third term in an A.P is15 and sum to 10 terms is125.find common difference and tenth term​

Answer 1

Step-by-step explanation:

given

third term of ap is 15

t3=15

a+2d = 15 -> Eq 1

sum of 10 terms in AP is 125

formula for sum of n terms = n/2(2a+(n-1)d)

S10 = 10/2(2a+(10-1)d)

125 = 5(2a+9d)

125 =10a+45d ->eq 2

solving equations 1 and 2

10a + 45d = 125

a + 2d = 15 -> multiply with 3

10a + 45d = 125

10a +20d = 150

- - -

=> 25d= -25

d= -25/25

d = -1

Substituting d = -1 in eq 1

a + 2d = 15

a+2(-1)=15

a-2=15

a=15+2

a=17

tenth term of AP

a+(n-1)d

t10 = 17+ (10-1) -1

t10= 17 + 9(-1)

t10= 17-9

t10 = 8