Question

the first term of the ap is12 .the number of terms is 15 and their sum is 390.find the common difference and the middle term​

Answer 1

Answer:

Common Difference = 2 and Middle term = 24

Step-by-step explanation:

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Here

a = 12

n = 15

Sn = 390

Therefore Sn = n/2 [2a + (n - 1)d]

Substitute the values in the above equation

We get

390 = 15/2 [2*12 + (15-1)d]

780 = 15 [24 + 14d]

52. = 24 + 14d

28. = 14d

d = 2

Therefore The common Difference is 2

We have 15 terms so the middle term will be 7th term

Therefore 7th term will be here n = 7 and d = 2

an = a + (n-1)d

a7 = 12 + (7-1)2

a7 = 12 + 6*2

a7 = 12 + 12

a7 = 24

Therefore the middle term is = 24