Great Southern Corp. raised its bid for Equitable General Corp. to $45 a share yesterday and the two companies announced final agreement to merge.

Great Southern, a Houston financial conglomerate had previously offered $40 a share for Equitable General, the McLean parent of Equitable General Life Insurance of Washington.

The new bid matched a $45 a share offer for Equitable General made last Friday by Liberty National Life Insurance of Birmingham.

Great Southern offered to pay cash for up to 1.2 million of the 2.8 million shares of Euitable General and to give the other stockholders one share of a convertible preferred stock, paying a $3 dividend and redeemable at $45 a share.

Great Southern said it planned to continue to operate Equitable General with its present officers, employes and Virginia headquarters.

Liberty National Chairman Frank Sanford Jr. said his company never received a response to its $45 a share offer. "I assume that means they're not interested " he said, adding, "at this point I don't know" if a counter offer will be made.

The critical difference in the two rival bids was not the price, but the possibility that many shareholders could receive stock rather than cash under the Great Southern plan.

Many Equitable General shareholders, including company insiders, have stock they have owned for years and which was purchased for as little as $1 a share. In a cash sale, they would be required to pay capital gains taxes - about 45 percent - on their profits, but a trade for stock is usually tax free.

A decision by the Internal Revenue Service on the tax consequences, approval of state and federal regulators, and the approval by shareholders of both companies are needed before the merger can be completed.

In raising the price of its offer to $45, Great Southern made one change in terms. The convertible preffered stock to be given for 1.6 million shares will be convertible into nine tenth of one share of Great Southern Common stock, rather than a full share. The shares are redsemable in cash for $45, starting at Great Southern's option, between 1989 and 1991.

Industry sources described the $45 offer as a fair price for Equitable General shares, which were traded in the $25 range before the prospect of a merger was raised and the stock soared toward the $45 range.

Equitable General's Executive Vice President Frank R. Eslinger said that how long it would, take to complete the merger is "question of mechanics"

Equitable General had earnings of $10 million last year on revenues of $47 million. Equitable General Life has about $1.4 billion if life insurance in force.

Great Southern earned $17 million last year on revenues of $124 million and has $3.2 billion of life insurance in force through Great Southern Life Insurance Co. The holding company also owns a savings and loan association, real estate developments and other interests.