Math, asked by venkateshmurthytlk, 1 day ago

if the middle term of the A.P is 300 then the sum of its first 51 terms is

Answers

Answered by dimplebadhe31

Answer:

510

Step-by-step explanation:

Let a be the 1st term and d be the common difference of an A.P.

T26=a+(26–1)d = 10. , or, a+25d = 10 ……………(1)

Sn = n/2.[ 2.a+(n-1).d]

S51= 51/2.[2a+(51–1)d] .

or, =(51/2).[2a+50d]

or, =( 51/2).2(a+25d) ,

or, = 51.(a+25.d). , putting a+25d=10 from eq.(1).

or, = 51×10= 510. , Answer.

Answered by brainlysme12

Explanation:

The difference between any two consecutive integers in an arithmetic progression (AP) sequence of numbers is always the same amount.
It also goes by the name Arithmetic Sequence.
If we look at our daily lives, we see arithmetic progression pretty frequently.
For instance, the number of days, weeks, or months in a year on the class roll.
Mathematicians refer to this pattern of series and sequences as progressions.

a^n = the nᵗʰ term in the sequence

a^1 = the first term in the sequence

d = the common difference between terms

Solution:

The mid term is T26 = 300

T1 =300 − 25d;

T 51 = 300 + 25d

S = 51/2 [300 − 25d + 300 + 25d]

51/2 [600]

= 15,300