Question

Sum of 1 st and 31st terms of an arithmetic sequence is 80.
a) What is the sum of 2nd and 30th terms?
b) What is the sum of 5th and 27 th terms?
c) What is the 16 th term?
d) What is the sum of first 31 terms?​

Answer 1

Solution :-

• A sequence is said to be in AP (Arithmetic Progression), if the difference between its consecutive terms are equal.

• The nth term of an AP is given as :-

T(n) = a + (n-1)•d , where a is the first term and d is the common difference.

• The common difference of an AP is given as :-

d = T(n) - T(n-1)

• The sum up to nth terms of an AP is given as :-

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

• The nth term of an AP is also given as :-

T(n) = S(n) - S(n-1)

So, let first term of given AP is a and common difference is d.

given that,

→ T(1) + T(31) = 80

→ a + [a + (31 - 1)d] = 80

→ 2a + 30d = 80

→ 2(a + 15d) = 80

→ a + 15d = 40 --------- Eqn.(1)

then,

→ T(2) + T(30)

→ [a + d] + [a + 29d]

→ 2a + 30d

→ 2(a + 15d)

→ 2 * 40

→ 80 (a) (Ans.)

and,

→ T(5) + T(27)

→ (a + 4d) + (a + 26d)

→ 2a + 30d

→ 2(a + 15d)

→ 2 * 40

→ 80 (b) (Ans.)

and,

→ T(16)

→ a + 15d

→ 40 (c) (Ans.)

and,

→ S(31)

→ (n/2)[first term + 31st term]

→ (31/2) * 80

→ 31 * 40

→ 1240 (d) (Ans.)

Learn more :-

evaluate the expression given by 83 - 81 + 87 - 85 +__________ + 395 - 393 + 399 - 397

https://brainly.in/question/14081691

If the nth term of an AP is (2n+5),the sum of first10 terms is

https://brainly.in/question/23676839

Answer 2

Given : Sum of 1 st and 31st terms of an arithmetic sequence is 80.

To Find :

a) What is the sum of 2nd and 30th terms?

b) What is the sum of 5th and 27 th terms?

c) What is the 16 th term?

d) What is the sum of first 31 terms?​

Solution :

AP

a , a + d , a , a + 2d

a is first term

nth term = a + (n - 1) d

Sum of 1 st and 31st terms of an arithmetic sequence is 80.

=> a + a + (31 - 1)d = 80

=> 2a + 30d = 80

=> a + 15d = 40

a + 15d is 16th term

hence 16th term  = 40

sum of 2nd and 30th terms

a + d + a + 29d  = 2a + 30d  = 80

sum of 5th and 27 th terms

= a + 4d + a + 26d =  2a + 30d  = 80

sum of first 31 terms

= (31/2)( 80)

= 31 * 40

= 1240

Learn More:

a,a+d,a+2d l and n terms of an AP find ( n-1)

brainly.in/question/7612734

FIRST term if an AP is 4 and the common difference is 3 its 12th term ...

brainly.in/question/7843059

a =3 d=101 Then For A.P Sn - Brainly.in

brainly.in/question/13170418