Question

Find the sum of the first 50 terms of the arithmetic sequence whose terms are 11,15,19,23......,

Answer 1

Step-by-step explanation:

sum of n terms: Sn

Sn formula: sum= n(2a+(n-1)d)/2

where, a= first term

d= common difference between two terms in AP

n= sum to no. of terms

given: a= 11

d= 15-11= 4

so, d=4

n= 50 (given)

so, by substituting the given values in the above formula.

Sn= 50(2(11)+(50-1)4)/2

Sn= 50(22+(49)4)/2

Sn= 50(22+196)/2

= 50(218)/2

= 25×218= 5450

so, sum to 50 terms= 5450.

Answer 2

$\bf\underline {\underline {\blue{Question :- }}}$

Find the sum of the first 50 terms of the arithmetic sequence whose terms are 11,15,19,23......,

$\bf\underline {\underline {\pink{Answer :- }}}$

a = 11

d = 15-11 = 4

n = 50

sum =

$\frac{n}{2} (2a + (n - 1)d)$

sum =

$\frac{50}{2} (2 \times (22 + 49 \times 4)) \\ 25(22 + 196) \\ 25 \times 218 = 5450$

So the sum of 50 terms of the given Ap sereis is 5450..