Question

Find four terms which are in G.P., whose third term is 4 more than first term and second term is 36 more than 4^th term.

Answer 1

Let first four terms of G.P. are a, ar, ar². ar³ where a is first term and r is common ratio.

According to question,

Third term = First term + 4

⇒ ar² = a + 4

⇒ a(r² – 1) = 4

According to question,

Second term = Fourth term + 36

⇒ ar = ar³ + 36

⇒ ar – ar³ = 36

⇒ ar(1 – r²) = 36

Divide equation (ii) by (i), we get

(ar(1 - r²))/(a(r² - 1)) = 36/4

⇒ – r = 9

⇒ r = – 9

Hence, common ratio of G.P.,
r = – 9

Putting r = – 9 in equation (i),

a[(-9)² – 1] = 4

⇒ a (81 – 1) = 4