Math, asked by XxZaraa89xX, 2 days ago

The 13th term of an ap is 4 times its 3rd term. If its 5th term is 16, find the sum of its first 15 terms.

Answers

Answered by ZubairSarookh

Answer:

HI ARMY OR non-army

Step-by-step explanation:

Formula

an= a+(n-1)d

Find the 13th term

a13 = a+12d

Find the 3rd term

a3= a+2d

13th term is 4times its 3rd term;

a+12d =4(a+2d)

a+12d =4a +8d

3a = 4d ----------------( i )equation

5th term is 16;

16 = a+4d

a= 16- 4d ---------------( ii )euation

Sub (i) into (ii);

3(16-4d) = 4d

48 -12d =4d

16d = 48

d=3 ------sub in equ ( ii)

Find a ;

a =16 -4d

a= 16- 4(3)

a = 4

find the nth term

an =a+(n-1)d

an = 4+(n-1)3

an = 4 +3n-3

an = 1+3n

Find the 15th term ;

a15 = 1 + 3(15)

a15 = 46

Find the sum of the first 10 terms;

Sn = $\frac{n}{2}$ (a+an)

S15 = $\frac{15}{2}$ (4+46)

S15 = 370

sooo done here is your answer

HOPE IT HELPS U MARK AS BRAINLIEST

Answered by vickysinghvikrant0