Question

Find 20th term from last in the AP 30, 21,12,……. If there are total 50 terms in the AP​

Answer 1

Answer: The formula for nth term of an AP is aₙ = a + (n - 1) d

Here, aₙ is the nth term, a is the first term, d is the common difference and n is the number of terms.

Third term of AP is a + (3 - 1)d = a + 2d

a + 2d = 12 .... (1)

Last term = 106

Thus, 50th term =106 [Since, n = 50]

a + (50 - 1)d = 106

a + 49d = 106... (2)

By solving equations (1) and (2) for the values of a and d,

a + 49d - (a + 2d) = 106 - 12

47d = 94

d = 2

Putting d = 2 in equation (1)

a + 2 × 2 = 12

a + 4 = 12

a = 12 - 4

a = 8

29th term of the AP is a₂₉ = a + (29 - 1)d

a₂₉ = 8 + (28) 2

a₂₉ = 8 + 56

a₂₉ = 64

Thus, 29th term of the AP is 64.

Step-by-step explanation:

Answer 2

Given A.P. series is 3, 8, 13, …, 253

Here, first term is a = 3

And common difference b/w terms is d = 8 - 3 = 5

Here last term is 253, So first of all we find out total number terms in the given series

as an = 253

• a + (n - 1)d = 253
• 3 + (n - 1)5 = 253
• (n - 1)5 = 250
• n - 1 = 50
• n = 51

so, there are 51 terms in given series.

Now, 20th term from last is = last term - mth term + 1 = 51 - 20 + 1 = 32

Now 32th term from first is

• a32 = a + (32 - 1)d
• a32 = 3 + 31*5
• a32 = 3 + 155
• a32 = 158

Hence , 20th term from last is 158