Question

n^th term of A.P. is a^n. If a^1 +a^2+a^3 = 102 and a^1 =15, then find a^10​

Answer 1

Answer:

186

Step-by-step explanation:

let the first three terms of AP be (a-d),a,(a+d)

=> a1= (a-d), a2= a, a3= (a+d)

Given that a1+a2+a3=102

=> (a-d)+a+(a+d)=102

=> 3a=102

hence a=34

also given tha a1=15

a-d=15

=> 34-d=15

=> d=19

now a1=15,a2=34,a3=53.....

=> a10= a+ 9d

= 15+9(19)

= 186

Answer 2

Answer:

The nth term of A.P is a_{10}a

10

= 216

Explanation:

n + n term = a_{n}a

n

= a+(n-1)d

a→ 1st term

d → common difference

a_{1}a

1

= a = 15

a_{2}a

2

= a+d = 15+d

a_{3}a

3

= a+2d = 15+2d

a_{1}a

1

+a_{2}a

2

+a_{3}a

3

= 102

15+15+d+15+2d = 102

3d = 102-45 = 67

d=67/3

a_{10}a

10

= a+(10-1)d

= a+2d

= 15 + 2 × \frac{67}{3}

3

67

= 15 + 201

= 216

Hence = a_{10}a

10

= 216

Step-by-step explanation:

HOPE IT HELPS YOU army