Question

The 10th term of an AP is 30 and the 15th term is 45. What is the Sum upto 10th term?​

Answer 1

Answer:

165

Step-by-step explanation:

given:

10th term of AP = 30

15th term of AP = 45

15th term = a+14d

10th term = a+9d

so,15th term - 10th term = a+14d-a-9d =5d = 45-30 =15

hence,5d = 15

so,d = 3

15th term = a+14d = a+14×3= a+42 = 45

hence,a = 45 - 42 = 3

sum upto 10th term = n/2(2a+(n-1)d)

here,a = 3,d = 3 and n = 10

so, sum upto 10th term =10/2(2×3 + (10-1)×3)

= 5(6 + 9×3) = 5(6+27) = 5×33 =165

hence,sum upto 10th term of AP is 165

Answer 2

Answer: 165

Explanation:

a10=a+9d=30..........(1)

a15=a+14d=45.........(2)

(2)-(1),

5d=15

d=15/5=3

put d=3 in (1)

ie, a+27=30

a=30-27= 3

S10= 10/2(3+30)

=5(33)

= 165

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