Question

Find the sums given below

(i) 7 + + 14 + ………… + 84

(ii) 34 + 32 + 30 + ……….. + 10

(iii) − 5 + (− 8) + (− 11) + ………… + (− 230)

Answer 1

(i)7 + + 14 + …………+ 84

For this A.P.,

a = 7

l = 84

Let 84 be the n^th term of this A.P.

l = a + (n − 1)d

22 = n − 1

n = 23

We know that,

(ii)34 + 32 + 30 + ……….. + 10

For this A.P.,

a = 34

d = a₂ − a₁ = 32 − 34 = −2

l = 10

Let 10 be the n^th term of this A.P.

l = a + (n − 1) d

10 = 34 + (n − 1) (−2)

−24 = (n − 1) (−2)

12 = n − 1

n = 13

(iii)(−5) + (−8) + (−11) + ………… + (−230)

For this A.P.,

a = −5

l = −230

d = a₂ − a₁ = (−8) − (−5)

= − 8 + 5 = −3

Let −230 be the n^th term of this A.P.

l = a + (n − 1)d

−230 = − 5 + (n − 1) (−3)

−225 = (n − 1) (−3)

(n − 1) = 75

n = 76

And,