Q) Find the 7th term from the end of AP 7, 10, 13, …, 184.

Ans:

Given AP series is:  7, 10, 13, ……. , 184

Step 1: Let’s identify first term and common difference of our given AP:

First term: a = 7

Common difference: d = 10 – 7 = 3

Step 2: Let’s find total terms in our AP:

The general formula for the n^th term is:

T_n = a + (n -1) d

∵ Given last term value = 184

∴ 184 = 7 + (n – 1) (3)

∴ 184 = 7 + 3 n – 3

∴ 177 = 3 n – 3

∴ 180 = 3n

∴  n = 60

So, the AP has 60 terms.

Step 3: Next, we find the 7^th term from the end:

∵ The k^th term from the end = (n – k + 1)^th term from start

Here, n = 60, k = 7

∴ 7^th term from the end = 60 + 1 – 7  = 54^th term from start

Step 4: Let’s calculate the value of 54^th term:

Since Value of n^th term, T_n = a + (n -1) d

∴ T₅₄ = 7 + ( 54 – 1) (3)

= 7 + 53 x 3 = 7 + 159 = 166

Therefore, the 7^th term from the end of the AP is 166.

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