Question

if root 2, root 8, root 18, root 32 in ap? if yes write three more times​

Answer 1

Answer:

here

a2 – a1 = √8 - √2 = √2(√4) - √2 = 2√2 - √2 = √2

a3 – a2 = √18 - √8 = √2(√9) - √2(√4) = 3√2 - 2√2 = √2

a4 – a3 = √32 - √18 = √2(√16) - √2(√9) = 4√2 - 3√2 = √2

For each term difference is same √2. So this sequence is an arithmetic progression and its common difference is d =√2 . Next four terms are :

⇒ a5 = a4 + d = √32 + √2 = 4√2 + √2 = 5√2 = √25(√2) = √50

⇒ a6 = a5 + d = √50 + √2 = 5√2 + √2 = 6√2 = √36(√2) = √72

⇒ a7 = a6 + d = √72 + √2 = 6√2 + √2 = 7√2 = √49(√2) = √98

⇒ a8 = a7 + d = √98 + √2 = 7√2 + √2 = 8√2 = √64(√2) = √128

Hence, Yes, d = √2, Next four terms are √50, √72, √98, √128.