Question

In an AP if the 12th term is -13 and the sum of its first four terms is 24 . Find the sum of its first 20 terms

Answer 1

Answer:

answer is 200 hope it helps you

Answer 2

$\underline{ \sf \fcolorbox{red}{pink}{ \huge{Solution :)}}}$

Given ,

• The 12th term of an AP is -13 , i.e a + 11d = - 13 --- (i)

• The sum of its first four terms is 24 , i.e 4a + 6d = 24 --- (ii)

Multiply equation (i) by 4 and (ii) by 1 , we get

4a + 44d = -52 --- (iii)

4a + 6d = 24 --- (iv)

Subtract equation (iii) from eq (iv) , we get

4a + 44d - (4a + 6d) = - 52 - 24

44d - 6d = -76

38d = -76

d = -2

Put the value of d = -2 in equation (i) , we get

a + 11(-2) = -13

a - 22 = -13

a = -13 + 22

a = 9

Now , the sum of first 20 terms of an AP is

$\sf \mapsto Sum = \frac{20}{2} \bigg(2(9) + (20 - 1)( - 2) \bigg) \\ \\\sf \mapsto Sum = 10(18 - 38) \\ \\\sf \mapsto Sum = 10(20) \\ \\\sf \mapsto Sum = 200$

Hence , the sum of first 20 terms of an AP is 200

_________ Keep Smiling ☺