Question

The sum of the 4th and 8th term of an arithmetic progression is 24 and the sum of the 6th and 10th term is 44. Find the sum of first 10 terms of the arithmetic progression.

Answer 1

according to the question

a4+a8=24-[1]

a4=a1+3d

and, a8=a1+7d

substituting the value in equation -[1]

hence, a1+3d+a1+7d=24

2a1+10d=24-[2]

a6=a1+5d

a10=a1+9d

a6+a10=44

hence, by substituting

a1+5d+a1+9d=44

2a1+14d=44-[3]

2a1=44-14d

substituting in equation-[2]

44-14d+10d=24

44-24=4d

20=4d

20/4=d

5=d

substituting in equation-[2]

2a1+10[5]=24

2a1+50=24

2a1=24-50

a1=-26/2

a1=13

hence, a1=13,d=5