Question

11. Find the sum of the series : 7+11+15+.........111

Answer 1

Answer:

1593

Step-by-step explanation:

Given series is increasing with a common difference of 15-11 = 11-7 = 4, which means it is an AP, with a = 7 & d = 4.

In APs, nth term = a + (n - 1)d.

Let the number of terms be n.

=> 111 = 7 + (n - 1)4

=> 27 = n

Using S = (n/2){2a + (n-1)d},

S = (27/2){2(7) + (27-1)4}

= (27/2){14 + 104}

= 1593

Answer 2

a = 7

d = 11 - 7 = 4

aₙ = 111

we know,

aₙ = a + (n - 1) d

111 = 7 + (n - 1) 4

111 - 7 = (n - 1) 4

104/4 = (n - 1)

26 = n - 1

n = 26 + 1

n = 27

Sₙ = n/2 (a + aₙ)

Sₙ = 27/2 (7 + 111)

= 27/2 × 118

= 27 × 59

= 1593

Therefore, Sum of the given series = 1593

Hope this helps! Thank you!