An important question from ML Agarwal (avichal publication) If sum of the 3rd and 8th term of an ap is 7 and the sum of the 7th and 14th term is -3.find the 10th term.

ML Publication, Class 10, Arithmetic Progression Chapter 9, question no. 16

# If sum of the 3rd and 8th term of an ap is 7 and the sum of the 7th and 14th term is -3.find the 10th term

Share

nth termÂ tnâ€‹=a+(nâˆ’1)d

a=Â First term

d=Â Common difference

n=Â number of terms

tnâ€‹=nthÂ term

## a3â€‹+a8â€‹=7a+2d+a+7d

## =72a+9d=7âŸ¶(i)

## a7â€‹+a14

## =âˆ’3a+6d+a+13d

## =âˆ’32a+19d=âˆ’3âŸ¶(ii)

FromÂ (i)Â &Â (ii)

2a+9d=72a+19d=âˆ’3

âˆ’10d=10d=âˆ’1,a=8.

a10â€‹=a+9d=8+9(âˆ’1)=âˆ’1