Question

What is the sum of first 10 terms of an AP if the first term is 1 and the
tenth term is 19?​

Answer 1

Given

first term is 1 and the tenth term is 19

To Find

Sum of first 10 terms of an ap

$\sf\huge\bold{\underline{\underline{{Solution}}}}$

We have first term (a) = 1

tenth term is 19

10th term = a+(10-1)d

=>19=a+9d

=>19=1 +9d

=>9d= 19-1

=>9d=18

=>d= 18/9

=>d=2

Hence,common difference(d) is 2.

We have to find sum of first 10 terms

means S₁₀

Sₙ= n/2[2a+(n-1)d]

=>S₁₀= 10/2[2a+(10-1)d]

=>S₁₀=5[2+9d]

=>S₁₀=5[2+9×2]

=>S₁₀=5[2+18]

=>S₁₀=5×20

=>S₁₀=100

Therefore ,sum of first 10 terms is 100