Question

Consider the arithmetic sequence whose 7th term is 34. and 15th term is 66

a) Find the common difference

b) Find the 20th term. ​

Answer 1

Given :- Consider the arithmetic sequence whose 7th term is 34. and 15th term is 66

a) Find the common difference .

b) Find the 20th term. .

Solution :-

we know that, an arithmetic sequence with first term as a and common difference as d , than

• nth term of AP is = a + (n - 1)d .

given that, 7th term of AP is 34 and 15th term is 66.

So,

→ T(7) = a + (7 - 1)d = 34

→ a + 6d = 34 -------- Eqn.(1)

and,

→ T(15) = a + (15 - 1)d = 66

→ a + 14d = 66 -------- Eqn.(2)

subtracting Eqn.(1) from Eqn.(2) we get,

→ (a + 14d) - (a + 6d) = 66 - 34

→ a - a + 14d - 6d = 32

→ 8d = 32

→ d = (32/8) = 4 (Ans.)

Putting value of d in Eqn.(1) ,

→ a + 6d = 34

→ a + 6*4 = 34

→ a + 24 = 34

→ a = 34 - 24

→ a = 10 .

Therefore,

→ T(20) = a + (20 - 1)d

→ T(20) = 10 + 19 * 4

→ T(20) = 10 + 76

→ T(20) = 86 (Ans.)

Hence, common difference is 4 and 20th term is 86.