Made easy test series

Question

Determine the first term of geometric progression is the sum of first term and third term is 40 and sum of second term and fourth term  is 80

1)12

2)16

3)8

4)4

Answer 1

Answer - 3. 8

Let a be the first term and r be the common ration of given GP –

GP : a, ar, ar^2, ar^3, ar^4, …

Sum of first and third term is 40 ie a + ar^2 = 40

      1. a(1 + r^2) = 40.

Sum of second and fourth term is 80 ie ar + ar^3 = 80

      2. ar(1 + r^2) = 80.

From 1 and 2 -  r (40) = 80, therefore r = 2.

From 1 - a(1 + 2^2) = 40, therefore a = 8.

Answer 2

Option: C

let, first term of G.P be “a” and common difference be “r”

i.e., 1^st term = a, 2^nd term = ar, 3^rd term = ar^2, 4^th term = ar^3.

given, sum of 1^st and 2^nd term = 40

a + ar^2 = 40 ----→ let it be equation 1.

and, sum of 2^nd and 4^th term = 80

ar + ar^3 = 80 -----→ let it be equation 2.

r(ar+ar^2) = 80 -------→ substitute equation 1 in equation 2

r (40) = 80

r = 80/40 = 2

r = 2

i.e., substitute r value in equation 1 or equation 2 to get the a value.

substituting in equation 1, gives:

a+a(2)^2 = 40

a+4a=40

5a=40

a=40/5

a=8.

Therefore the first term of Geometric preogression is 8.