Question

if the 8th term of an ap is 31 and the 15th term is 16 more than the 11th term .
1. find the AP
2.find the sum of first 15 sum​

Answer 1

Answer:

let a be the 1st term and d be the common difference

a8 = a + 7d = 31  

a15 = a + 14d = a11 + 16

(a + 10d) + 16

a + 10d +16 = a + 14d  

= a + 10d +16 = a + 10d + 4d

= 16 = 4d  

d = 16/4 = 4

a + 7d = 31

a + 7(4) = 31

a + 28 = 31  

a = 31 -28 = 3

a = 3 , d = 4 ...

therefore Ap = a , a+d , a+2d ,a+3d ......

= 3 , 3+4 ,3+2(4) , 3 + 3(4)

= 3 , 7 , 11 , 15 .......

2. S15=  15/2 [ 2[3] + [14] [4] ]

         =15/2 [ 6 + 56]

         =15/2 [ 62

         =15 [ 31]

         =465

hope it helped

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