Question

First and last term of A.P. are 2 and 34

respectively. Sum of its term is 90

these value of n will be

(a) 3 (b) 4 (c) 5 (d) 6​

Answer 1

Answer:

a1= 2

an = 34

Sum of Ap =n/2(a1 + an)

Ie, n/2 ( 2+ 34) = 90

180/n = 36

36n= 180

n = 180/36

n = 5

Step-by-step explanation:

Answer 2

ANSWER:

• The value of n = 5

GIVEN:

• First term = 2

• Last term = 34

• Sum of the terms = 90

TO FIND:

• The value of n

EXPLANATION:

$\bold{\large{S_n = n/2(a + l)}}$

a = 2

l = 34

$S_n$ = 90

90 = n/2(2 + 34)

180 = 36 n

18 n = 90

9 n = 45

n = 5

HENCE THE VALUE OF n = 5

VERIFICATION:

$\large{\bold{n = \dfrac{l - a}{d} + 1}}$

n = 5

l = 34

a = 2

$5 = \dfrac{34 - 2 + d}{d}$

5d = 32 + d

4d = 32

d = 8

$\bold{\large{S_n= n/2(2a + (n - 1) d)}}$

n = 5

a = 2

d = 8

$S_n$ = 5/2(2(2) + (5 - 1) 8)

$S_n$ = 5/2(4 + (4) 8)

$S_n$ = 5/2(4(1 + 8))

$S_n$ = 5(2 × 9)

$S_n$ = 5(18)

$S_n$ = 90

HENCE VERIFIED.